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<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within [[Risk analysis]]. It has been around for about 50 years, and in all those years, it has changed very little, as what is does is both rather basic but at the same time very powerful: FTA provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
<br />
<br />
= Big Idea =<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|thumb|right|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
<br />
= Applications =<br />
FTA is widely applicable concept that can be used in many different cases. Currently, it is primarily used within System Safety and Reliability Engineering, where it is widely applied by many firms, including NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref> and the US nuclear energy sector.<ref name=ureg>US.NRC: Fault Tree Handbook, visited the 28/9, 2015, [[http://www.nrc.gov/reading-rm/doc-collections/nuregs/staff/sr0492/]]</ref>. Typically, there are two types of fault trees - "simple" Fault trees that involve basic symbols, and Advanced fault trees that involves more complicated symbols. Both of these concepts will be explained in the sections below.<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event. These calculations are done through <ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, of each limitation as well as an elaboration on each subject.<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until these events are discovered, or at the very least, forcing one to recalculate the probabilities when more events shows up. <ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
=Conclusion=<br />
All in all, FTA is a very powerful tool that can be applied to many different areas. It does possess some limitations, mainly that Fault trees can easily become huge and confusing, thus defeating one of the prime purposes which is to provide an overview. With that said, though, the strengths more than make up for those limitations that cannot be worked around. Furthermore, FTA is widely used, meaning that there are many computer tools for assisting in developing FTAs, allowing for much easier calculation of the probability of the top event, as well as calculating the minimal cut set, too. Finally, these tools can also check the consistency of the fault tree, making sure that the fault tree created actually makes sense.<br />
<br />
<br />
= Annotated Bibliography =<br />
http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html :Provides a brief overview over the fault tree analysis concept, as well as another example of FTA.<br />
<br />
http://www.weibull.com/basics/fault-tree/ : Provides an intermediary overview over the FTA concept, both in terms of concept and application. Also provides further references for more reading.<br />
<br />
http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf : Nasa's handbook to building fault trees - a very in depth description of the concepts as well as how to apply them.<br />
<br />
http://www.weibull.com/hotwire/issue63/relbasics63.htm :Provides a more in-depth description of what a minimal cut set is<br />
<br />
<br />
<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17482Fault tree analysis2015-09-28T21:03:48Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within [[Risk analysis]]. It has been around for about 50 years, and in all those years, it has changed very little, as what is does is both rather basic but at the same time very powerful: FTA provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
<br />
<br />
= Big Idea =<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|thumb|right|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event. These calculations are done through <ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, of each limitation as well as an elaboration on each subject.<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until these events are discovered, or at the very least, forcing one to recalculate the probabilities when more events shows up. <ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
=Conclusion=<br />
All in all, FTA is a very powerful tool that can be applied to many different areas. It does possess some limitations, mainly that Fault trees can easily become huge and confusing, thus defeating one of the prime purposes which is to provide an overview. With that said, though, the strengths more than make up for those limitations that cannot be worked around. Furthermore, FTA is widely used, meaning that there are many computer tools for assisting in developing FTAs, allowing for much easier calculation of the probability of the top event, as well as calculating the minimal cut set, too. Finally, these tools can also check the consistency of the fault tree, making sure that the fault tree created actually makes sense.<br />
<br />
<br />
= Annotated Bibliography =<br />
http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html :Provides a brief overview over the fault tree analysis concept, as well as another example of FTA.<br />
<br />
http://www.weibull.com/basics/fault-tree/ : Provides an intermediary overview over the FTA concept, both in terms of concept and application. Also provides further references for more reading.<br />
<br />
http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf : Nasa's handbook to building fault trees - a very in depth description of the concepts as well as how to apply them.<br />
<br />
http://www.weibull.com/hotwire/issue63/relbasics63.htm :Provides a more in-depth description of what a minimal cut set is<br />
<br />
<br />
<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17481Fault tree analysis2015-09-28T21:03:36Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within [[Risk analysis]]. It has been around for about 50 years, and in all those years, it has changed very little, as what is does is both rather basic but at the same time very powerful: FTA provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
<br />
<br />
= Big Idea =<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|thumb|right|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event. These calculations are done through <ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, of each limitation as well as an elaboration on each subject.<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until these events are discovered, or at the very least, forcing one to recalculate the probabilities when more events shows up. <ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
=Conclusion=<br />
All in all, FTA is a very powerful tool that can be applied to many different areas. It does possess some limitations, mainly that Fault trees can easily become huge and confusing, thus defeating one of the prime purposes which is to provide an overview. With that said, though, the strengths more than make up for those limitations that cannot be worked around. Furthermore, FTA is widely used, meaning that there are many computer tools for assisting in developing FTAs, allowing for much easier calculation of the probability of the top event, as well as calculating the minimal cut set, too. Finally, these tools can also check the consistency of the fault tree, making sure that the fault tree created actually makes sense.<br />
<br />
<br />
= Annotated Bibliography =<br />
http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html :Provides a brief overview over the fault tree analysis concept, as well as another example of FTA.<br />
<br />
http://www.weibull.com/basics/fault-tree/ : Provides an intermediary overview over the FTA concept, both in terms of concept and application. Also provides further references for more reading.<br />
<br />
http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf : Nasa's handbook to building fault trees - a very in depth description of the concepts as well as how to apply them.<br />
<br />
http://www.weibull.com/hotwire/issue63/relbasics63.htm :Provides a more in-depth description of what a minimal cut set is<br />
<br />
<br />
<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17473Fault tree analysis2015-09-28T21:00:58Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within [[Risk analysis]]. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|thumb|right|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event. These calculations are done through <ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, of each limitation as well as an elaboration on each subject.<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until these events are discovered, or at the very least, forcing one to recalculate the probabilities when more events shows up. <ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
=Conclusion=<br />
All in all, FTA is a very powerful tool that can be applied to many different areas. It does possess some limitations, mainly that Fault trees can easily become huge and confusing, thus defeating one of the prime purposes which is to provide an overview. With that said, though, the strengths more than make up for those limitations that cannot be worked around. Furthermore, FTA is widely used, meaning that there are many computer tools for assisting in developing FTAs, allowing for much easier calculation of the probability of the top event, as well as calculating the minimal cut set, too. Finally, these tools can also check the consistency of the fault tree, making sure that the fault tree created actually makes sense.<br />
<br />
<br />
= Annotated Bibliography =<br />
http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html :Provides a brief overview over the fault tree analysis concept, as well as another example of FTA.<br />
<br />
http://www.weibull.com/basics/fault-tree/ : Provides an intermediary overview over the FTA concept, both in terms of concept and application. Also provides further references for more reading.<br />
<br />
http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf : Nasa's handbook to building fault trees - a very in depth description of the concepts as well as how to apply them.<br />
<br />
http://www.weibull.com/hotwire/issue63/relbasics63.htm :Provides a more in-depth description of what a minimal cut set is<br />
<br />
<br />
<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17449Fault tree analysis2015-09-28T20:49:10Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within [[Risk analysis]]. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|thumb|right|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event. These calculations are done through <ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, of each limitation as well as an elaboration on each subject.<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
=Conclusion=<br />
All in all, FTA is a very powerful tool that can be applied to many different areas. It does possess some limitations, but the strengths more than make up for those limitations that cannot be worked around. Furthermore, FTA is widely used, meaning that there are many computer tools for assisting in developing FTAs, allowing for much easier calculation of the probability of the top event, as well as calculating the minimal cut set, too. Finally, these tools can also check the consistency of the fault tree, making sure that the fault tree created actually makes sense.<br />
<br />
<br />
= Annotated Bibliography =<br />
http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html :Provides a brief overview over the fault tree analysis concept, as well as another example of FTA.<br />
<br />
http://www.weibull.com/basics/fault-tree/ : Provides an intermediary overview over the FTA concept, both in terms of concept and application. Also provides further references for more reading.<br />
<br />
http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf : Nasa's handbook to building fault trees - a very in depth description of the concepts as well as how to apply them.<br />
<br />
http://www.weibull.com/hotwire/issue63/relbasics63.htm :Provides a more in-depth description of what a minimal cut set is<br />
<br />
<br />
<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17446Fault tree analysis2015-09-28T20:48:37Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within [[Risk analysis]]. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|thumb|right|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event. These calculations are done through <ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, of each limitation as well as an elaboration on each subject.<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
=Conclusion=<br />
All in all, FTA is a very powerful tool that can be applied to many different areas. It does possess some limitations, but the strengths more than make up for those limitations that cannot be worked around. Furthermore, FTA is widely used, meaning that there are many computer tools for assisting in developing FTAs, allowing for much easier calculation of the probability of the top event, as well as calculating the minimal cut set, too. Finally, these tools can also check the consistency of the fault tree, making sure that the fault tree created actually makes sense.<br />
<br />
<br />
= Annotated Bibliography =<br />
http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html :Provides a brief overview over the fault tree analysis concept, as well as another example of FTA.<br />
<br />
<ref name="http://www.weibull.com/basics/fault-tree/">http://www.weibull.com/basics/fault-tree/</ref>: Provides an intermediary overview over the FTA concept, both in terms of concept and application. Also provides further references for more reading.<br />
<br />
<ref name="http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf">http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf</ref>: Nasa's handbook to building fault trees - a very in depth description of the concepts as well as how to apply them.<br />
<br />
<ref name="http://www.weibull.com/hotwire/issue63/relbasics63.htm">http://www.weibull.com/hotwire/issue63/relbasics63.htm</ref>:Provides a more in-depth description of what a minimal cut set is<br />
<br />
<br />
<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17444Fault tree analysis2015-09-28T20:48:07Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within [[Risk analysis]]. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|thumb|right|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event. These calculations are done through <ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, of each limitation as well as an elaboration on each subject.<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
=Conclusion=<br />
All in all, FTA is a very powerful tool that can be applied to many different areas. It does possess some limitations, but the strengths more than make up for those limitations that cannot be worked around. Furthermore, FTA is widely used, meaning that there are many computer tools for assisting in developing FTAs, allowing for much easier calculation of the probability of the top event, as well as calculating the minimal cut set, too. Finally, these tools can also check the consistency of the fault tree, making sure that the fault tree created actually makes sense.<br />
<br />
<br />
= Annotated Bibliography =<br />
[[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html"]]http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html</ref>Provides a brief overview over the fault tree analysis concept, as well as another example of FTA.<br />
<br />
<ref name="http://www.weibull.com/basics/fault-tree/">http://www.weibull.com/basics/fault-tree/</ref>: Provides an intermediary overview over the FTA concept, both in terms of concept and application. Also provides further references for more reading.<br />
<br />
<ref name="http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf">http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf</ref>: Nasa's handbook to building fault trees - a very in depth description of the concepts as well as how to apply them.<br />
<br />
<ref name="http://www.weibull.com/hotwire/issue63/relbasics63.htm">http://www.weibull.com/hotwire/issue63/relbasics63.htm</ref>:Provides a more in-depth description of what a minimal cut set is<br />
<br />
<br />
<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17442Fault tree analysis2015-09-28T20:47:36Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within [[Risk analysis]]. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|thumb|right|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event. These calculations are done through <ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, of each limitation as well as an elaboration on each subject.<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
=Conclusion=<br />
All in all, FTA is a very powerful tool that can be applied to many different areas. It does possess some limitations, but the strengths more than make up for those limitations that cannot be worked around. Furthermore, FTA is widely used, meaning that there are many computer tools for assisting in developing FTAs, allowing for much easier calculation of the probability of the top event, as well as calculating the minimal cut set, too. Finally, these tools can also check the consistency of the fault tree, making sure that the fault tree created actually makes sense.<br />
<br />
<br />
= Annotated Bibliography =<br />
<ref name="http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html">http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html</ref>Provides a brief overview over the fault tree analysis concept, as well as another example of FTA.<br />
<br />
<ref name="http://www.weibull.com/basics/fault-tree/">http://www.weibull.com/basics/fault-tree/</ref>: Provides an intermediary overview over the FTA concept, both in terms of concept and application. Also provides further references for more reading.<br />
<br />
<ref name="http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf">http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf</ref>: Nasa's handbook to building fault trees - a very in depth description of the concepts as well as how to apply them.<br />
<br />
<ref name="http://www.weibull.com/hotwire/issue63/relbasics63.htm">http://www.weibull.com/hotwire/issue63/relbasics63.htm</ref>:Provides a more in-depth description of what a minimal cut set is<br />
<br />
<br />
<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17438Fault tree analysis2015-09-28T20:44:20Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within [[Risk analysis]]. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|thumb|right|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event. These calculations are done through <ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, of each limitation as well as an elaboration on each subject.<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
=Conclusion=<br />
All in all, FTA is a very powerful tool that can be applied to many different areas. It does possess some limitations, but the strengths more than make up for those limitations that cannot be worked around. Furthermore, FTA is widely used, meaning that there are many computer tools for assisting in developing FTAs, allowing for much easier calculation of the probability of the top event, as well as calculating the minimal cut set, too. Finally, these tools can also check the consistency of the fault tree, making sure that the fault tree created actually makes sense.<br />
<br />
<br />
= Annotated Bibliography =<br />
[[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]: Provides a brief overview over the fault tree analysis concept, as well as another example of FTA.<br />
<br />
<br />
[[http://www.weibull.com/basics/fault-tree/]]: Provides an intermediary overview over the FTA concept, both in terms of concept and application. Also provides further references for more reading.<br />
<br />
<br />
[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]: Nasa's handbook to building fault trees - a very in depth description of the concepts as well as how to apply them.<br />
<br />
<br />
[[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]: Provides a more in-depth description of what a minimal cut set is<br />
<br />
<br />
<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17197Fault tree analysis2015-09-28T19:29:33Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within [[Risk analysis]]. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|thumb|right|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, of each limitation as well as an elaboration on each subject.<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
= Annotated Bibliography =<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17191Fault tree analysis2015-09-28T19:28:19Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within [[Risk analysis]]. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|thumb|right|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
= Annotated Bibliography =<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17190Fault tree analysis2015-09-28T19:27:04Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|thumb|right|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
= Annotated Bibliography =<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17188Fault tree analysis2015-09-28T19:26:41Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|right|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
= Annotated Bibliography =<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17186Fault tree analysis2015-09-28T19:26:26Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|right|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|center|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
= Annotated Bibliography =<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17184Fault tree analysis2015-09-28T19:25:39Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|thumb|link=http://apppm.man.dtu.dk/images/a/ab/Fault_Tree_example.jpg|center|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
= Annotated Bibliography =<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=17180Fault tree analysis2015-09-28T19:24:45Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
All in all, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|300px|thumb|center|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury. To enlarge, please click the picture.]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
= Annotated Bibliography =<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Talk:The_Gantt_chart_and_the_usage_nowadays&diff=12855Talk:The Gantt chart and the usage nowadays2015-09-22T17:32:30Z<p>S113440: </p>
<hr />
<div>Josef: Hello, I like your idea. See if the "chronology" idea makes sense - if the Gantt chart changed significantly over the years, then this may be interesting. Otherwise, you could for example also discuss how other project management methods related to Gantt charts (e.g. how it needs a WBS, relationship to network plans, critical path etc.)<br />
<br />
Jacob:<br />
First of all, a very interesting article. It's following the structure, which is a good thing in my book, and the introduction gives us a clear overview of what it is we have to read. Nevertheless, I do have some comments:<br />
<br />
*1 reference only is too few- you need to find more references to back up what you are saying!<br />
*I'd suggest a spellcheck - your article is understandable, but there are some spelling errors, mainly in the Limitations section, that makes understanding more difficult<br />
*I would maybe suggest the term "History" instead of "Throwback", considering that this is a scientific article, and throwback seems more like slang to me<br />
*The first example of a Gant chart presented here needs some text commenting it<br />
*Your reference to PERT/CPN is fine, but I would add another reference at the bottom of your page and refer to this as well.<br />
*I would probably list the benefits before the drawbacks and rename the section to something else than Limitations, since benefits aren't really a part of the limitations.<br />
*One of the drawbacks mentioned is that gant charts cannot be printed out on normal paper anymore due to their size, and you say this is not a drawback anymore "because of technology". This seems to be a gross simplification, and I would certainly still call this a drawback, since most still prefers to have various diagrams and such printed out and to have them physically during meetings, rather than just see them on a screen.<br />
*In drawbacks, at the end, you say that several drawbacks have been eliminated with time, or are not as significant in the past. Since this is a document aimed at the present, perhaps only list those that are still relevant today, and move the others to the a "past drawbacks"?</div>S113440http://13.50.150.85/index.php?title=Talk:Lean_in_Project_Management&diff=12828Talk:Lean in Project Management2015-09-22T17:01:33Z<p>S113440: </p>
<hr />
<div>Mette: I like the idea and the topic you have chosen. Lean contains many tools, so you could maybe consider if you should focus on only one tool in case of not getting your hands too full. It would still be possible to look at the questions you have presented by only looking at one tool.<br />
<br />
== Feedback ==<br />
<br />
s113440 - Jacob:<br />
*First of all, I'd say this is a very good article, obviously, a lot of work has been put into it, and it's written in an engaging way. With that said, it's also very long, and some chapters are missing, so I'd really recommend removing anything deemed unnecessarry - perhaps a section such as the "Relay race" may be removed? (It's a pretty common type of race I think)<br />
*Generally clear of spelling errors and proper punctionation, there are a few, though, so I'd suggest spellchecking the document. A common mistake made two or three times is using "Further", rather than "Furthermore" (such as section: Lean Project Management, sentence: "Further Reusch identified examples of waste in projects in relation to the categories of waste introduced above. The results are shown below."<br />
*In section Lean Thinking, I would be very careful with starting out with such a statement that most would think Toyota when they hear lean. I'm pretty sure I could find many that wouldn't - for instance, even though the company I currently work in (ATP) uses Lean quite a bit, I'm doubtful anyone would know where it originates from.<br />
*Figure 2 almost fills the entire screen - I'd suggest either putting the two diagrams on top of eachother (old type of project management with the critical chain first, then the new way), or alternatively just centering the figure and letting the text come below and above it. Even if you do decide to keep it in the way it is, I would suggest flipping the two figures - it initially caused me some confusion to see the Critical Path first, then the Critical chain, and think: "Hmm, Lean seems to be doing this in a worser way than normal..." (I read left to right = old to new)<br />
*The article seems based on many different sources, which is a good thing. All of them seems credible, too.<br />
<br />
s141569 – Review to article “Lean in Project Management”<br />
<br />
Peer review started at 18:00<br />
<br />
I find the article really interesting because it is referring in something that I did not really know about. It is a good chance to read something about lean and how it is used in project management and moreover in a company like Toyota.<br />
<br />
I would suggest to the author to add some more examples to be more visible the way of using it. Moreover, it is not clear if the implementation is the same with the application. I would recommend to avoid unnecessary information because the article is going to be very long and hard to be read. <br />
<br />
*The article in general is free of errors except few syntax errors in some sentences.<br />
* It is written in an engaging style because I did not know a lot about this topic, so it attracted me to read it. <br />
*The structure is very good in small and understandable sentences. <br />
*The figures are not so many but they are clear, they are referred in the text and finally they are helpful in the section that they have been put. There is no reference if they are borrowed from somewhere (copyright)<br />
*The article is properly formatted but with no hyper-links from Wikipedia. The graphics are used, are the photos that I referred above. There is no video in the article.<br />
*According to the providing information, I believe that it is very interesting for a practitioner.<br />
*I think that the article is related to a project, program or portfolio management topic.<br />
*I think that the article is going to be very long and hard to be read because the length is almost 3.000 words and there are 2 chapters missing until the finish.<br />
*There is a logical flow among the parts of the article.<br />
*The starting summary describes what follows on extend.<br />
*There are both sources and references.<br />
*The article is based on different kind of resources. All of them I think they are of high quality.<br />
*There is no link with other relevant pages in apppm wiki.</div>S113440http://13.50.150.85/index.php?title=Talk:Management_of_risk&diff=12804Talk:Management of risk2015-09-22T16:32:30Z<p>S113440: </p>
<hr />
<div>Reviewer 2: Jacob<br />
<br />
*Before the final deliverance, I would suggest a thorough spell- and gramma check, as well as revamping where you set full stops, since there are many unnecessarry and wrongfully placed full stops, which severely limits the readability (Example: ""chance or probability of loss". Meaning that only negative results could" - the full stop should in this case have been a comma, if anything)<br />
*Secondly, parts of a website is called sections, not chapters, for the unwritten reference you have. You also have a few other references that haven't been created yet - I would suggest removing the references and possibly just giving a short description of what you're referring to instead (For instance, COntingency in the "For Projects" section).<br />
*Next, you're not following the structure of the article as supposed - I'm not sure how much of a problem that is, though, since the alternative structure you have used make sense to me, and also includes many of the requirements from the description (i.e. Introduction, limitations, Big idea (although renamed)). <br />
*I would also suggest a few more figures, for instance of Fault Trees, or some of the other methods, just to give a different visual effect.<br />
*Finally, I would elaborate on the subjects of the General methodology, the Important principles and the benefits, making them more than just a set of bullet points.<br />
<br />
Reviewer 1: Lea<br />
*You are following the Method-article type. The general outline of your article gives good guidance to the topic. I am missing a bit of the application or implementation part.<br />
*Structure: There is a good structure but the “abstract” in the beginning and the first heading introduction are not very clear. A short summary of the article would be good. Also an abstract should not exceed 200 words. <br />
*Introduction. It is said that one ISO guide complements the other. Is this information relevant? Maybe an explanation of why you start out with the ISO guide.<br />
* There are a few spelling mistakes, but your sentences are short and can be easily read. <br />
*The figure in the beginning cannot be read. Maybe change the pixel size. If you do not have more complimentary figures, I think it is fine. Otherwise one or two more pictures would give a better overview. <br />
*The subject is interesting and definitely corresponds to the course subject. Since there are still some Headings without text, I guess you are not done writing yet. For the further progress I would suggest to try and get more “grip” on the topic. Narrow it down in the end to maybe one tool. <br />
*Sources are unfortunately a little sparse. I would suggest to get more information from relevant articles or books. <br />
*Annotated bibliography has not yet been added. <br />
*Some words are highlighted in the text but they are just linked to a blank page. Maybe you wanted to link the text to other wiki articles?</div>S113440http://13.50.150.85/index.php?title=Talk:Management_of_risk&diff=12803Talk:Management of risk2015-09-22T16:32:22Z<p>S113440: </p>
<hr />
<div>Reviewer 2: Jacob<br />
<br />
*Before the final deliverance, I would suggest a thorough spell- and gramma check, as well as revamping where you set full stops, since there are many unnecessarry and wrongfully placed full stops, which severely limits the readability (Example: ""chance or probability of loss". Meaning that only negative results could" - the full stop should in this case have been a comma, if anything)<br />
*Secondly, parts of a website is called sections, not chapters, for the unwritten reference you have. You also have a few other references that haven't been created yet - I would suggest removing the references and possibly just giving a short description of what you're referring to instead (For instance, COntingency in the "For Projects" section).<br />
*Next, you're not following the structure of the article as supposed - I'm not sure how much of a problem that is, though, since the alternative structure you have used make sense to me, and also includes many of the requirements from the description (i.e. Introduction, limitations, Big idea (although renamed)). I would also suggest a few more figures, for instance of Fault Trees, or some of the other methods, just to give a different visual effect.<br />
*Finally, I would elaborate on the subjects of the General methodology, the Important principles and the benefits, making them more than just a set of bullet points.<br />
<br />
Reviewer 1: Lea<br />
*You are following the Method-article type. The general outline of your article gives good guidance to the topic. I am missing a bit of the application or implementation part.<br />
*Structure: There is a good structure but the “abstract” in the beginning and the first heading introduction are not very clear. A short summary of the article would be good. Also an abstract should not exceed 200 words. <br />
*Introduction. It is said that one ISO guide complements the other. Is this information relevant? Maybe an explanation of why you start out with the ISO guide.<br />
* There are a few spelling mistakes, but your sentences are short and can be easily read. <br />
*The figure in the beginning cannot be read. Maybe change the pixel size. If you do not have more complimentary figures, I think it is fine. Otherwise one or two more pictures would give a better overview. <br />
*The subject is interesting and definitely corresponds to the course subject. Since there are still some Headings without text, I guess you are not done writing yet. For the further progress I would suggest to try and get more “grip” on the topic. Narrow it down in the end to maybe one tool. <br />
*Sources are unfortunately a little sparse. I would suggest to get more information from relevant articles or books. <br />
*Annotated bibliography has not yet been added. <br />
*Some words are highlighted in the text but they are just linked to a blank page. Maybe you wanted to link the text to other wiki articles?</div>S113440http://13.50.150.85/index.php?title=Talk:Management_of_risk&diff=12802Talk:Management of risk2015-09-22T16:32:09Z<p>S113440: </p>
<hr />
<div>Reviewer 2: Jacob<br />
<br />
*Before the final deliverance, I would suggest a thorough spell- and gramma check, as well as revamping where you set full stops, since there are many unnecessarry and wrongfully placed full stops, which severely limits the readability (Example: ""chance or probability of loss". Meaning that only negative results could" - the full stop should in this case have been a comma, if anything)<br />
*Secondly, parts of a website is called sections, not chapters, for the unwritten reference you have. You also have a few other references that haven't been created yet - I would suggest removing the references and possibly just giving a short description of what you're referring to instead (For instance, COntingency in the "For Projects" section).<br />
*Next, you're not following the structure of the article as supposed - I'm not sure how much of a problem that is, though, since the alternative structure you have used make sense to me, and also includes many of the requirements from the description (i.e. Introduction, limitations, Big idea (although renamed)).<br />
I would also suggest a few more figures, for instance of Fault Trees, or some of the other methods, just to give a different visual effect.<br />
*Finally, I would elaborate on the subjects of the General methodology, the Important principles and the benefits, making them more than just a set of bullet points.<br />
<br />
Reviewer 1: Lea<br />
*You are following the Method-article type. The general outline of your article gives good guidance to the topic. I am missing a bit of the application or implementation part.<br />
*Structure: There is a good structure but the “abstract” in the beginning and the first heading introduction are not very clear. A short summary of the article would be good. Also an abstract should not exceed 200 words. <br />
*Introduction. It is said that one ISO guide complements the other. Is this information relevant? Maybe an explanation of why you start out with the ISO guide.<br />
* There are a few spelling mistakes, but your sentences are short and can be easily read. <br />
*The figure in the beginning cannot be read. Maybe change the pixel size. If you do not have more complimentary figures, I think it is fine. Otherwise one or two more pictures would give a better overview. <br />
*The subject is interesting and definitely corresponds to the course subject. Since there are still some Headings without text, I guess you are not done writing yet. For the further progress I would suggest to try and get more “grip” on the topic. Narrow it down in the end to maybe one tool. <br />
*Sources are unfortunately a little sparse. I would suggest to get more information from relevant articles or books. <br />
*Annotated bibliography has not yet been added. <br />
*Some words are highlighted in the text but they are just linked to a blank page. Maybe you wanted to link the text to other wiki articles?</div>S113440http://13.50.150.85/index.php?title=Talk:Management_of_risk&diff=12801Talk:Management of risk2015-09-22T16:31:49Z<p>S113440: </p>
<hr />
<div>Reviewer 2: Jacob<br />
<br />
Before the final deliverance, I would suggest a thorough spell- and gramma check, as well as revamping where you set full stops, since there are many unnecessarry and wrongfully placed full stops, which severely limits the readability (Example: ""chance or probability of loss". Meaning that only negative results could" - the full stop should in this case have been a comma, if anything)<br />
<br />
Secondly, parts of a website is called sections, not chapters, for the unwritten reference you have. You also have a few other references that haven't been created yet - I would suggest removing the references and possibly just giving a short description of what you're referring to instead (For instance, COntingency in the "For Projects" section).<br />
<br />
Next, you're not following the structure of the article as supposed - I'm not sure how much of a problem that is, though, since the alternative structure you have used make sense to me, and also includes many of the requirements from the description (i.e. Introduction, limitations, Big idea (although renamed)).<br />
I would also suggest a few more figures, for instance of Fault Trees, or some of the other methods, just to give a different visual effect.<br />
<br />
Finally, I would elaborate on the subjects of the General methodology, the Important principles and the benefits, making them more than just a set of bullet points.<br />
<br />
Reviewer 1: Lea<br />
*You are following the Method-article type. The general outline of your article gives good guidance to the topic. I am missing a bit of the application or implementation part.<br />
*Structure: There is a good structure but the “abstract” in the beginning and the first heading introduction are not very clear. A short summary of the article would be good. Also an abstract should not exceed 200 words. <br />
*Introduction. It is said that one ISO guide complements the other. Is this information relevant? Maybe an explanation of why you start out with the ISO guide.<br />
* There are a few spelling mistakes, but your sentences are short and can be easily read. <br />
*The figure in the beginning cannot be read. Maybe change the pixel size. If you do not have more complimentary figures, I think it is fine. Otherwise one or two more pictures would give a better overview. <br />
*The subject is interesting and definitely corresponds to the course subject. Since there are still some Headings without text, I guess you are not done writing yet. For the further progress I would suggest to try and get more “grip” on the topic. Narrow it down in the end to maybe one tool. <br />
*Sources are unfortunately a little sparse. I would suggest to get more information from relevant articles or books. <br />
*Annotated bibliography has not yet been added. <br />
*Some words are highlighted in the text but they are just linked to a blank page. Maybe you wanted to link the text to other wiki articles?</div>S113440http://13.50.150.85/index.php?title=Talk:Management_of_risk&diff=12800Talk:Management of risk2015-09-22T16:31:31Z<p>S113440: </p>
<hr />
<div>Reviewer 2: Jacob<br />
Before the final deliverance, I would suggest a thorough spell- and gramma check, as well as revamping where you set full stops, since there are many unnecessarry and wrongfully placed full stops, which severely limits the readability (Example: ""chance or probability of loss". Meaning that only negative results could" - the full stop should in this case have been a comma, if anything)<br />
Secondly, parts of a website is called sections, not chapters, for the unwritten reference you have. You also have a few other references that haven't been created yet - I would suggest removing the references and possibly just giving a short description of what you're referring to instead (For instance, COntingency in the "For Projects" section).<br />
Next, you're not following the structure of the article as supposed - I'm not sure how much of a problem that is, though, since the alternative structure you have used make sense to me, and also includes many of the requirements from the description (i.e. Introduction, limitations, Big idea (although renamed)).<br />
I would also suggest a few more figures, for instance of Fault Trees, or some of the other methods, just to give a different visual effect.<br />
Finally, I would elaborate on the subjects of the General methodology, the Important principles and the benefits, making them more than just a set of bullet points.<br />
<br />
Reviewer 1: Lea<br />
*You are following the Method-article type. The general outline of your article gives good guidance to the topic. I am missing a bit of the application or implementation part.<br />
*Structure: There is a good structure but the “abstract” in the beginning and the first heading introduction are not very clear. A short summary of the article would be good. Also an abstract should not exceed 200 words. <br />
*Introduction. It is said that one ISO guide complements the other. Is this information relevant? Maybe an explanation of why you start out with the ISO guide.<br />
* There are a few spelling mistakes, but your sentences are short and can be easily read. <br />
*The figure in the beginning cannot be read. Maybe change the pixel size. If you do not have more complimentary figures, I think it is fine. Otherwise one or two more pictures would give a better overview. <br />
*The subject is interesting and definitely corresponds to the course subject. Since there are still some Headings without text, I guess you are not done writing yet. For the further progress I would suggest to try and get more “grip” on the topic. Narrow it down in the end to maybe one tool. <br />
*Sources are unfortunately a little sparse. I would suggest to get more information from relevant articles or books. <br />
*Annotated bibliography has not yet been added. <br />
*Some words are highlighted in the text but they are just linked to a blank page. Maybe you wanted to link the text to other wiki articles?</div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=11490Fault tree analysis2015-09-21T20:08:41Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|1000px|center|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum. It also allows for calculating the probability of the top event happening if the probability of the base events is known.<ref name=asq>QP: What is a Fault Tree Analysis?, visited the 21/9, 2015, [[http://asq.org/quality-progress/2002/03/problem-solving/what-is-a-fault-tree-analysis.html]]</ref><br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events. Furthermore, FTA has not changed much in the recent times - the biggest changes seems to be in terms of which gates are excluded, for instance, the Danish standard's guide to FTA<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref> uses fewer gates and events when compared to, for instance, NASA<ref name=NASA>NASA - Fault Tree Handbook with Aerospace Applications, accessed the 21/9, 2015[[http://www.hq.nasa.gov/office/codeq/doctree/fthb.pdf]]</ref>.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
= Annotated Bibliography =<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=11375Fault tree analysis2015-09-21T19:40:27Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept and purpose==<br />
FTA is a top down analysis where one identifies the undesired state, obtains information about the rest of the system and how various events are related to the undesired state, and from this knowledge, a fault tree is produced. This tree consists of various events and gates, with the undesired event being on the top - also referred to as the top event as a result - and base events at the bottom, with various other events distributed inbetween. All of these events are connected by various gates, all with specific purposes based in Logic. To further understand these Fault trees, an example below has been provided.<br />
<br />
[[File:Fault_Tree_example.jpg|1000px|center|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
As a result of the structure of Fault trees, with the events connected by logical gates, Boolean algebra can be applied to them once the Tree has been fully developed. This allows for further analysis of the fault tree, possibly reducing its size through a method known as "The Minimal cut set", which will be explained later in this article. This Boolean algebra is part of its purpose - it allows for various defined rules, while still allowing the author of the Fault tree a great degree of flexibility in depicting the Top event as well as the entire system, thus allowing for a good overview of all relations within the system connected to the top event, while still allowing for methods to reduce the complexity to the bare minimum.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
= Annotated Bibliography =<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=10915Fault tree analysis2015-09-21T17:28:33Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediate events and draws their connection to the top event through various gates, and finally, once all intermediate events have been discovered and the base events are reached, these are added as the root of the trees.<br />
[[File:Fault_Tree_example.jpg|1000px|center|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<ref name=weibullMCS>Weibull Minimal Cut Set, visited the 13/9, 2015, [[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]</ref><br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
= Annotated Bibliography =<br />
<references/></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=10910Fault tree analysis2015-09-21T17:25:39Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediate events and draws their connection to the top event through various gates, and finally, once all intermediate events have been discovered and the base events are reached, these are added as the root of the trees.<br />
[[File:Fault_Tree_example.jpg|1000px|center|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref><ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]</ref> These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
= Annotated Bibliography =<br />
<references/><br />
<br />
<br />
<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015. Provides further details on FTA<br />
<br />
[[http://www.weibull.com/hotwire/issue63/relbasics63.htm]], visited the 20/9, 2015. Explains what a minimum cut set is in detail.<br />
<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=10909Fault tree analysis2015-09-21T17:24:53Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediate events and draws their connection to the top event through various gates, and finally, once all intermediate events have been discovered and the base events are reached, these are added as the root of the trees.<br />
[[File:Fault_Tree_example.jpg|1000px|center|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events<ref name=weibullFT>Weibull Fault Analysis, visited the 13/9, 2015, [[http://www.weibull.com/basics/fault-tree/]]. These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
= Annotated Bibliography =<br />
<references/><br />
<br />
<br />
<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015. Provides further details on FTA<br />
<br />
[[http://www.weibull.com/hotwire/issue63/relbasics63.htm]], visited the 20/9, 2015. Explains what a minimum cut set is in detail.<br />
<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=10898Fault tree analysis2015-09-21T17:21:56Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediate events and draws their connection to the top event through various gates, and finally, once all intermediate events have been discovered and the base events are reached, these are added as the root of the trees.<br />
[[File:Fault_Tree_example.jpg|1000px|center|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events. These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done..<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
= Annotated Bibliography =<br />
<references/><br />
<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010. The Danish standard for risk management techniques, provides the Danish standard on how to do FTA.<br />
<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015. Provides further details on FTA<br />
<br />
[[http://www.weibull.com/hotwire/issue63/relbasics63.htm]], visited the 20/9, 2015. Explains what a minimum cut set is in detail.<br />
<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=10895Fault tree analysis2015-09-21T17:21:23Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediate events and draws their connection to the top event through various gates, and finally, once all intermediate events have been discovered and the base events are reached, these are added as the root of the trees.<br />
[[File:Fault_Tree_example.jpg|1000px|center|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events. These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model. <br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' Domino effects, which are low-probability, high-consequence accidents, are not easily depicted in FTA due to the fact that all symbols are the same size, each symbol do not show how bad the consequences are, and will only show the probability, which, by the very nature of these effects, are considered to be low.<ref name=RiskMan>Risk management - Risk Assesment Techniques, Dansk Standard, 2010</ref><br />
<br />
<br />
= Annotated Bibliography =<br />
<references/><br />
<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010. The Danish standard for risk management techniques, provides the Danish standard on how to do FTA.<br />
<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015. Provides further details on FTA<br />
<br />
[[http://www.weibull.com/hotwire/issue63/relbasics63.htm]], visited the 20/9, 2015. Explains what a minimum cut set is in detail.<br />
<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=10864Fault tree analysis2015-09-21T17:11:49Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediate events and draws their connection to the top event through various gates, and finally, once all intermediate events have been discovered and the base events are reached, these are added as the root of the trees.<br />
[[File:Fault_Tree_example.jpg|1000px|center|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
==Basic fault trees==<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The basic figures of a fault tree]]<br />
A basic fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events.<br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event.<br />
<br />
==Advanced Fault trees==<br />
Once a user has understood how to make the basic fault trees, there exist several additional type of gates, as well as two additional events. These are as follows:<br />
<br />
'''Gates:'''<br />
<br />
*'''Voting Or:''' Voting Or acts as a normal Or gate, except that "k" or more input events must be true before output occurs. Symbol: Like an Or-gate, with "k" in the middle, where k is an integer with the amount of inputs that must occur for the output to happen.<br />
*'''XOR, also known as Exclusive Or:''' Exclusive Or is a gate that only allows the output to happen if and only if one input is true and all other inputs are false. Symbol: An Or-gate symbolized inside an And-gate<br />
*'''Priority And:''' This type of gate lets the output occur if the input happens in a specific sequence. Depiction varies, but typically like an And-gate with an extra flat line in the bottom.<br />
*'''Inhibit:''' Inhibit gates allows for a certain output to happen in case the input occurs while an enabling condition is also true. Depiction: A hexagon with inputs from below, outputs on top, and conditioning events from the side.<br />
<br />
'''Events:'''<br />
<br />
*'''External Event:''' An event that is assumed to occur, always. Traditionally has a fixed probability of either 0 or 1. Depiction: A square with a triangle on top.<br />
*'''Conditioning Event:''' This type of event typically occurs in combination with Inhibit gates, but can actually be used in combination with any other gate as well, setting a specific condition for the gate that it is applied to. Depiction: An ellipse that is layig down.<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model. <br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' <br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010. The Danish standard for risk management techniques, provides the Danish standard on how to do FTA.<br />
<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015. Provides further details on FTA<br />
<br />
[[http://www.weibull.com/hotwire/issue63/relbasics63.htm]], visited the 20/9, 2015. Explains what a minimum cut set is in detail.<br />
<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=10242Fault tree analysis2015-09-21T11:42:52Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediate events and draws their connection to the top event through various gates, and finally, once all intermediate events have been discovered and the base events are reached, these are added as the root of the trees.<br />
[[File:Fault_Tree_example.jpg|1000px|center|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The figures of a fault tree]]<br />
A fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events. <br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event<br />
<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model. <br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees. This means that a component that fails partially, such as a Tank Rupture in Figure 1 (thus failing), but no oil spills out (but only fails partially), cannot be depicted.<br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA. Furthermore, every tree may be split up into multiple trees through the link, such as Figure 1, but even with this as well, Figure 1 is still a large and complex tree.<br />
<br />
'''FTAs do not easily enable domino effects:''' <br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010. The Danish standard for risk management techniques, provides the Danish standard on how to do FTA.<br />
<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015. Provides further details on FTA<br />
<br />
[[http://www.weibull.com/hotwire/issue63/relbasics63.htm]], visited the 20/9, 2015. Explains what a minimum cut set is in detail.<br />
<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=10214Fault tree analysis2015-09-21T11:16:37Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediate events and draws their connection to the top event through various gates, and finally, once all intermediate events have been discovered and the base events are reached, these are added as the root of the trees.<br />
[[File:Fault_Tree_example.jpg|1000px|center|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The figures of a fault tree]]<br />
A fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events. <br />
<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event<br />
<br />
<br />
= Strengths =<br />
FTA possess several strengths. These are as follows:<br />
<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
To elaborate, FTA has a highly systematic, disciplined approach when it comes to modelling. Typically, such models are inflexible when it comes to modelling many different factors - however, FTA allows for precisely this, thus remaining flexible as well. Furthermore, the structure of FTA allows for several strengths, too: First of all, the fact that FTA is a top down approach means that the attention of the analysis is automatically focused on failures directly related to the top event. Secondly, since the structure allows for displaying all interfaces and interactions in the analysed system, it is very useful in systems that possess many of such interfaces and interactions, simply because it allows for a nice overview of all the interactions between these. In a more general sense, the structure of FTA actually allow the viewer an easy understanding of cause and effect in any system that it is applied to, however, larger systems may need to be split up into several trees to keep this easy understanding property alive. Finally, FTA enables logic analysis to be applied on the fault trees due to the fact that there are only binary states, thus allowing for the minimal cut set to be found, allowing for a simple way of finding failure pathways that might otherwise have been missed.<br />
<br />
= Limitations =<br />
Just as FTA has several strengths, so there are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''Large'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model<br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees<br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
<br />
'''Large:''' As systems grows more complex, so will the fault trees. As a result, in the modern time where many systems are interlinked, fault trees might easily become very large and complex to both generate, understand and work with. Various computer tools can reduce this effect, but such tools must first be obtained and understood, thus reducing the effect of the simplicity of FTA.<br />
<br />
'''FTAs do not easily enable domino effects:''' <br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010. The Danish standard for risk management techniques, provides the Danish standard on how to do FTA.<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015. Provides further details on FTA<br />
[[http://www.weibull.com/hotwire/issue63/relbasics63.htm]], visited the 20/9, 2015. Explains what a minimum cut set is in detail.<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=9989Fault tree analysis2015-09-20T18:33:15Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediate events and draws their connection to the top event through various gates, and finally, once all intermediate events have been discovered and the base events are reached, these are added as the root of the trees.<br />
[[File:Fault_Tree_example.jpg|1000px|center|Figure 1: A fault tree from a Shale Gas case depicting the risks associated with worker injury]]<br />
<br />
Figure 1 shows a fully developed fault tree. It is rather large fault tree, however, but it shows how one can choose a top event and then, through developing each intermediate event, reach the bottom of the tree. The triangles, in this particular case, refers to other fault trees developed in this case, and including these would have made the tree even larger and would have been counterproductive.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The figures of a fault tree]]<br />
A fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events are the roots of the tree, and denoted BE1, BE2, BE....., BE13, for the 13 different base events in that specific case.<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediate events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
These 6 symbols are then used by defining the top event (also known as the undesired event) and breaking down what events could cause this event. Once these events have been identified and paired with the top event through and- or Or-gates, the next round of intermediate events are broken down into new intermediate events and connected through gates. This process continues until further analysis is unproductive, thus resulting in base events. <br />
<br />
Once a fault tree has been finished, a minimal cut set can be calculated. This minimal cut set is a set of the minimum amount of base events that will cause the top event - in the example of Figure 3, the minimal cut set is either {1, 2, 3} or {1, 2, 4} since either of these three events together will cause the top event. What makes these cut sets especially neat are the fact that they give an easy overview over the easiest path to the top event, and these minimum cut sets also displays which basic events are both necessary and sufficient to produce the top event. This minimum cut set can then be used to generate a new fault tree, and through this fault tree, provided that the probability of the base events are known, it is possible to calculate the probability of the top event<br />
[[File:Minimumcutset.png|300px|thumb|right|Figure 3: Minimal cut set example]]<br />
<br />
= Strengths =<br />
*'''Highly systematic, disciplined, flexible approach'''<br />
*'''Attention on failures directly related to top event'''<br />
*'''Displays all interfaces and interactions in systems'''<br />
*'''Easy understanding of the cause and effect'''<br />
*'''Provides a method to do logic analysis on the top event'''<br />
<br />
= Limitations =<br />
There are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediate events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model<br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees<br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
<br />
'''FTAs do not easily enable domino effects:''' <br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010. The Danish standard for risk management techniques, provides the Danish standard on how to do FTA.<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015. Provides further details on FTA<br />
[[http://www.weibull.com/hotwire/issue63/relbasics63.htm]], visited the 20/9, 2015. Explains what a minimum cut set is in detail.<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=File:Minimumcutset.png&diff=9805File:Minimumcutset.png2015-09-20T16:13:37Z<p>S113440: </p>
<hr />
<div></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=9763Fault tree analysis2015-09-20T15:47:16Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediary events and draws their connection to the top event through various gates, and finally, once all intermediary events have been discovered and the base events are reached, these are added as the root of the trees.<br />
<br />
[[File:Fault_Tree_example.jpg|1000px|center|Figure 1: A fault tree]]<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The figures of a fault tree]]<br />
A fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events....<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediary events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
<br />
= Limitations =<br />
There are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediary events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model<br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees<br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
<br />
'''FTAs do not easily enable domino effects:''' <br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=9762Fault tree analysis2015-09-20T15:46:59Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediary events and draws their connection to the top event through various gates, and finally, once all intermediary events have been discovered and the base events are reached, these are added as the root of the trees.<br />
<br />
[[File:Fault_Tree_example.jpg|800px|center|Figure 1: A fault tree]]<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The figures of a fault tree]]<br />
A fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events....<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediary events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
<br />
= Limitations =<br />
There are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediary events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model<br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees<br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
<br />
'''FTAs do not easily enable domino effects:''' <br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=9761Fault tree analysis2015-09-20T15:46:33Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediary events and draws their connection to the top event through various gates, and finally, once all intermediary events have been discovered and the base events are reached, these are added as the root of the trees.<br />
<br />
[[File:Fault_Tree_example.jpg|600px|Figure 1: A fault tree]]<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The figures of a fault tree]]<br />
A fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events....<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediary events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
<br />
= Limitations =<br />
There are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediary events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model<br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees<br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
<br />
'''FTAs do not easily enable domino effects:''' <br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=9759Fault tree analysis2015-09-20T15:46:18Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediary events and draws their connection to the top event through various gates, and finally, once all intermediary events have been discovered and the base events are reached, these are added as the root of the trees.<br />
<br />
[[File:Fault_Tree_example.jpg|600px|thumb|Figure 1: A fault tree]]<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The figures of a fault tree]]<br />
A fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events....<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediary events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
<br />
= Limitations =<br />
There are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediary events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model<br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees<br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
<br />
'''FTAs do not easily enable domino effects:''' <br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=File:Fault_Tree_example.jpg&diff=9754File:Fault Tree example.jpg2015-09-20T15:44:50Z<p>S113440: </p>
<hr />
<div></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=9748Fault tree analysis2015-09-20T15:37:45Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediary events and draws their connection to the top event through various gates, and finally, once all intermediary events have been discovered and the base events are reached, these are added as the root of the trees.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The figures of a fault tree]]<br />
A fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events....<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediary events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
<br />
= Limitations =<br />
There are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediary events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model<br />
<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees<br />
<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
<br />
'''FTAs do not easily enable domino effects:''' <br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=9744Fault tree analysis2015-09-20T15:34:30Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks. <br />
<br />
This article will consist of four sections:<br />
<br />
*'''Big Idea:''' This section will explain the concept of FTA, as well as show an example of a fully developed Fault tree. It will also briefly explain the history of FTA.<br />
*'''Applications:''' This section will explain how to use FTA.<br />
*'''Limitations:''' This section will explore the limitations of FTA.<br />
*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediary events and draws their connection to the top event through various gates, and finally, once all intermediary events have been discovered and the base events are reached, these are added as the root of the trees.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|Figure 2: The figures of a fault tree]]<br />
A fault tree consists of 6 different symbols. Of these, two are gates and 4 are events, as seen by figure 2.<br />
*And gate: An And gate has two or more inputs and one output. If all inputs are true, then the output will be true as well, thus causing the event above the gate, but if just one event is false, the event above will not happen<br />
*Or gate: Or gates are mostly the same as And gates - where they differ is that only one input has to be true to cause the above event, and all inputs has to be false to not cause the above event<br />
*Base event: An event that is not analysed further, meaning that it could either not be broken down into further detail, or doing so would be counter-productive. In the example of figure 1, base events....<br />
*Event that is not analysed further: This group of events are usually events that lack data, meaning that further analysis is meaningless.<br />
*Event that is analysed further: Intermediary events that are analysed further.<br />
*Event analysed on a different page: Used as a link to make huge Fault trees into smaller trees, allowing for a better overlook.<br />
<br />
<br />
= Limitations =<br />
There are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediary events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
'''FTAs do not easily enable domino effects:''' <br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=9716Fault tree analysis2015-09-20T15:16:27Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediary events and draws their connection to the top event through various gates, and finally, once all intermediary events have been discovered and the base events are reached, these are added as the root of the trees.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|alt text]]<br />
A fault tree consists of 6 different symbols, as seen by figure x<br />
*And gate:<br />
*Or gate:<br />
*Base event:<br />
*Event that is not analysed further:<br />
*Event that is analysed further:<br />
*Event analysed on a different page:<br />
<br />
<br />
= Limitations =<br />
There are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediary events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
'''FTAs do not easily enable domino effects:''' <br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=9715Fault tree analysis2015-09-20T15:15:11Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediary events and draws their connection to the top event through various gates, and finally, once all intermediary events have been discovered and the base events are reached, these are added as the root of the trees.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
[[File:SymbolsOfFaultTrees.png|300px|thumb|right|alt text]]<br />
A fault tree consists of 6 different symbols, as seen by figure x<br />
*And gate<br />
*Or gate<br />
*Base event<br />
*Event that is not analysed further<br />
*Event that is analysed further<br />
*Event analysed on a different page<br />
<br />
<br />
= Limitations =<br />
There are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediary events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
'''FTAs do not easily enable domino effects:''' <br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=File:SymbolsOfFaultTrees.png&diff=9714File:SymbolsOfFaultTrees.png2015-09-20T15:14:14Z<p>S113440: Shows the various symbols of fault trees</p>
<hr />
<div>Shows the various symbols of fault trees</div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=9711Fault tree analysis2015-09-20T15:12:30Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediary events and draws their connection to the top event through various gates, and finally, once all intermediary events have been discovered and the base events are reached, these are added as the root of the trees.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
A fault tree consists of 6 different symbols:<br />
*And gate<br />
*Or gate<br />
*Base event<br />
*Event that is not analysed further<br />
*Event that is analysed further<br />
*'''Event analysed on a different page'''<br />
<br />
<br />
= Limitations =<br />
There are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediary events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
'''FTAs do not easily enable domino effects:''' <br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=9706Fault tree analysis2015-09-20T15:08:56Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks.<br />
<br />
= Big Idea =<br />
==Concept==<br />
FTA is a top down analysis where one identifies the undesired state and places it as the top event, then goes through all intermediary events and draws their connection to the top event through various gates, and finally, once all intermediary events have been discovered and the base events are reached, these are added as the root of the trees.<br />
<br />
==History==<br />
Fault tree diagrams were originally invented in 1962 by the Bell Telephone Laboratories. They did this on behalf of the US Air Force in connection with the Minuteman ICBM launch control system. It was very succesful, and were subsequently adopted by the Boing Company, then the US army, then US government and, in today's world, it is used widely in System Safety and Reliability Engineering, as well as many other major fields of engineering, and can be applicated to almost any project that needs to know the effect of various events and how they connect with other events.<br />
<br />
<br />
= Applications =<br />
A fault tree consists of 6 different symbols:<br />
*'''And gate'''<br />
*'''Or gate'''<br />
*'''Base event'''<br />
*'''Event that is not analysed further'''<br />
*'''Event that is analysed further'''<br />
*'''Event analysed on a different page'''<br />
<br />
<br />
= Limitations =<br />
There are several limitations in the FTA model. Below follows a brief overview, followed by an elaboration on each subject.<br />
*'''Uncertainties in the probabilities of the top event'''<br />
*'''The whole picture is not discovered'''<br />
*'''FTAs are a static model'''<br />
*'''Fault trees only possess binary states'''<br />
*'''Human error is not easily included'''<br />
*'''FTAs do not easily enable domino effects'''<br />
<br />
'''Uncertainties in the top event:''' Due to the fact that the probability of the top event is calculated from the probability of the base event and the interconnected events, if the probability of the base events are not known accurately, it will cause uncertainty in the rest of the system.<br />
'''The whole picture is not discovered:''' Sometimes, causal events are not discovered, or intermediary events are missing, thus creating a fault tree that does not cover the entire system. In this case, it prevents probability analysis until the events are discovered.<br />
'''FTAs are a static model:''' Since FTAs are static models, time is not taken into account in the model<br />
'''Fault trees only possess binary states:''' Fault trees only possess binary states, and as such, partial failures cannot be represented in these trees<br />
'''Human error is not easily included:''' Since human error varies greatly, and since Fault trees only posses binary states, one either has to include a lot of different events to compensate for possible human failure, which clouds up the diagrams, or simplify it with a simple "Human error" state, which does not show the complete picture. As such, showing human error in fault trees is not easily done.<br />
'''FTAs do not easily enable domino effects:''' <br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=8176Fault tree analysis2015-09-13T13:07:11Z<p>S113440: </p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Fault tree analysis (Hereby noted as FTA) is a technique primarily used within Risk analysis. It provides a visual representation of an undesired event, as well as the dependencies of said event, thereby allowing one to identify and analyse what factors can contribute to this event, also called base events. Finally, it allows one to calculate the probabilities of the top event.<br />
Unfortunately, the FTA has certain limitations, as with all models, and as such, they are not sufficient alone to analyse all risks in a project. Nevertheless, FTA is a very powerful tool in managing risks, and allows for good visualizations of events and allows a displined, highly systematic, flexible approach to analysing these risks.<br />
<br />
= Big Idea =<br />
<br />
<br />
= Applications =<br />
<br />
<br />
= Limitations =<br />
<br />
<br />
= Annotated Bibliography =<br />
Risk Management - Risk Assesment Techniques, Dansk Standard, 2010<br />
[[http://www.weibull.com/basics/fault-tree/]], visited the 13/9, 2015<br />
<br />
<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440http://13.50.150.85/index.php?title=Articles_Fall_Term_2015&diff=8141Articles Fall Term 20152015-09-13T12:29:05Z<p>S113440: /* Overview of 2015 Wiki Articles */</p>
<hr />
<div>Please complete this table with your name, user name and the title of your article.<br />
<br />
To create more lines in the table click '''Edit''' and use the following code to create more lines in the table and replace the example text with your own information:<br />
<br />
<pre style="white-space: pre-wrap; <br />
white-space: -moz-pre-wrap; <br />
white-space: -pre-wrap; <br />
white-space: -o-pre-wrap; <br />
word-wrap: break-word;"><br />
|Gkatzalas<br />
|Nikolaos<br />
|s141569<br />
|http://apppm.man.dtu.dk/index.php/The_Gantt_chart_and_the_usage_nowadays#Abstract<br />
|-<br />
<br />
Create a direct link by making square brackets around the title [[The Gantt chart and the usage nowadays]] (Case sensitive)<br />
<br />
The straight lines ( | ) create columns and the straight line with a dash ( |- ) creates a new row in the table.<br />
( |} ) is only used at the very end to finish the coding for the table.<br />
</pre><br />
<br />
<br />
=Overview of 2015 Wiki Articles=<br />
<br />
{| class="wikitable sortable"<br />
|+Fall 2015 Wiki Articles<br />
|-<br />
!Gkatzalas<br />
!Nikolaos<br />
!s141569<br />
![[The Gantt chart and the usage nowadays]]<br />
|-<br />
|Filis<br />
|Charalampos<br />
|Ch.filis<br />
|[[Project Management with Gantt-Charts]]<br />
|-<br />
|Larsen<br />
|Leonora<br />
|s112910<br />
|[[Gantt Charts as a Tool for Project Management]]<br />
|-<br />
|Sala Vilar<br />
|Lluís Ròmul<br />
|s141586<br />
|[[Portfolio Management in a Startup]]<br />
|-<br />
|Pitsavas<br />
|Konstantinos<br />
|Konspits<br />
|[[Modularisation: A modern process for project management]]<br />
|-<br />
|Kampianakis<br />
|Andreas<br />
|s150912<br />
|[[Financial Portfolio Optimization Methods]]'''<br />
|-<br />
|Penzes<br />
|Balint<br />
|s141943<br />
|[[Product development and portfolio management processes at LEGO]]<br />
|-<br />
|Hozmache<br />
|Mihaela<br />
|s146898<br />
|[[Risk Management]]'''<br />
|-<br />
|Le Corre<br />
|Damien<br />
|Damien<br />
|[[Game theory in project management]]'''<br />
|-<br />
|Bertrand<br />
|Fabien<br />
|150477<br />
|[[Multi project management]]'''<br />
|-<br />
|Cassel<br />
|Sara<br />
|Sarac<br />
|[[The benefits of systems engineering]]'''<br />
|-<br />
|Sergi<br />
|Gibaja Musachs<br />
|S141926<br />
|[[Rapid Application Development in Extreme Project Management]]'''<br />
|-<br />
|Poza<br />
|María<br />
|s150793<br />
|[[Integrated Cost and Schedule Control]]'''<br />
|-<br />
|Kulikova<br />
|Nataliia<br />
|s140767<br />
|SCRUM Method<br />
|-<br />
|Pekala<br />
|Adam<br />
|Adam.pekala<br />
|[[Critical Path Method in Construction Industry]]<br />
|-<br />
|Garnotel<br />
|Gaëtan<br />
|gaetangarnotel<br />
|[[V-Model]]<br />
|-<br />
|Ghanizada<br />
|Naweed<br />
|S103745<br />
|[[PRINCE2, A Project Management Methodology]]<br />
|-<br />
|Jacobsen<br />
|Martin<br />
|MistaJacob<br />
|Article Title and Link here<br />
|-<br />
|Ferraresi<br />
|Fabrizio<br />
|S150905<br />
|Projects in Controlled Environments, a process-based approach for project management<br />
|-<br />
|Tanghus<br />
|Bjarke<br />
|S113815<br />
|Location Based Scheduling<br />
|-<br />
|Højgaard Hindhede<br />
|Daniel <br />
|S143352 <br />
|[[ Critical path optimization in construction management]]<br />
|-<br />
|Gayot<br />
|Charles-Henri<br />
|s141074<br />
|[[Responsibility Assignment Matrix (RACI Matrix)]]<br />
|-<br />
|Thorp Sørensen<br />
|Anders<br />
|s103183<br />
|The Gantt Chart<br />
|-<br />
|Makris<br />
|Dimitrios<br />
|Dimak<br />
|Benchmarking in Project Management<br />
|-<br />
|Greiling<br />
|Lea<br />
|Lea<br />
|[[Lean in Project Management]]<br />
|-<br />
|Latorre Duque<br />
|Ana<br />
|Ana<br />
| [[Modularity and Black-Boxing]]<br />
|-<br />
|Almanzi<br />
|Stefano<br />
|S141530<br />
| Work Breakdown Structure (WBS)<br />
|-<br />
|Montagner<br />
|Giacomo<br />
|S150821<br />
|[[Scrum Metodology in the Agile Project Management]]<br />
|-<br />
|Ruiz Muñoz<br />
|Gustavo Adolfo<br />
|S150821<br />
| [[Lean 6 Sigma in project management]]<br />
|-<br />
|Kalmus<br />
|Thomas<br />
|S141938<br />
| [[Program evaluation and review technique (PERT) ]]<br />
|-<br />
|Gudmundsson<br />
|Arnar Gauti<br />
|S141543<br />
|Program management in change management<br />
|-<br />
|Jacobsen<br />
|Ian Thobias<br />
|S113735<br />
|[[Story Points Estimation]]<br />
|-<br />
|Gibaja Musachs<br />
|Sergi<br />
|S141926<br />
|Rapid Application Development in Extreme Project Management<br />
|-<br />
|Otiv<br />
|Peter<br />
|s145166<br />
|Managing Uncertainty and Risk in a Project<br />
|-<br />
|Boesgaard<br />
|Katrine<br />
|KB1991<br />
|[[Gantt Chart]]<br />
|-<br />
|Sorth-Olsen<br />
|Rasmus<br />
|Sorth90<br />
|[[Lean as a project management tool]]<br />
|-<br />
|Salling<br />
|Stephanie<br />
|StephSalling<br />
|Management in E. Pihl & Søn A/S<br />
|-<br />
|Ruina<br />
|Jessica Linda<br />
|Jejenji <br />
|[[Scheduling techniques in Project Management]]<br />
|-<br />
|Gjerstrup<br />
|Jacob<br />
|s113440<br />
|[[Fault tree analysis]]<br />
|-<br />
|Lynge<br />
|Jane<br />
|s997303<br />
|Theory of Constraint in project management<br />
|-<br />
|Palmerini<br />
|Alessandro<br />
|alex161<br />
|Project Management Communication <br />
|-<br />
|Tvedt<br />
|Ida Marie<br />
|IMT<br />
|[[BREEAM - project management and sustainable development]]<br />
|-<br />
|Søndenaa<br />
|Mathilde Hanssen<br />
|s150621<br />
|[[Critical chain project management (CCPM)]]<br />
|-<br />
|Thorning-Schmidt<br />
|Nanna<br />
|Nannats<br />
|[[Earned Value Management]]<br />
|-<br />
|Rasmussen<br />
|Marie-Louise<br />
|DI2009<br />
|Article title and Link here<br />
|-<br />
|-<br />
|Lara Hoces<br />
|Fernando<br />
|s131882<br />
|The Oticon Case<br />
|-<br />
|Christos<br />
|Stamatis<br />
|S145170<br />
|[[Olympic Games London 2012: When the client strives for innovation (The London model)]]'''<br />
|-<br />
|Moe<br />
|Elizabeth Lindhard<br />
|113129<br />
|[[Contracting as a PM]]<br />
|-<br />
|Lessis<br />
|Vasileios<br />
|lessisv<br />
|[[Rational Unified Process (RUP)]]<br />
|-<br />
|Klibo Buur<br />
|Christian<br />
|s117409<br />
|[[Project Execution Model (PEM)]]<br />
|-<br />
|Bachmann<br />
|Thomas<br />
|s117318<br />
|[[Lean Tools in Project Management]]<br />
|-<br />
|Vilar Bustos<br />
|Alberto<br />
|s142581<br />
|[[Minimizing Risk and Uncertainties in Construction Projects]]<br />
|-<br />
|Trap Wiegandt<br />
|Sissel<br />
|s112195<br />
|[[Using Kotters Framework for Change Management Projects]]<br />
|-<br />
|Christensen<br />
|Britt Marie Lekven<br />
|brittmch<br />
|[[Lean in building and construction industry]]<br />
|-<br />
|Vestergaard Andersen<br />
|Andreas<br />
|AndreasAndersen<br />
|Management of Project Changes<br />
|-<br />
|Ann-Elise<br />
|Gustavsen<br />
|Alise<br />
|[[Stakeholder Analysis and Matrices ]]<br />
|-<br />
|Krogh<br />
|Daniel<br />
|DanielKrogh<br />
|[[Managing Uncertainty and Risk on the Project]]<br />
|-<br />
|Viig<br />
|Oliver Johannes<br />
|s102935<br />
|[[BIM as a project management tool]]<br />
|-<br />
|Federico<br />
|Sbernini<br />
|s141573<br />
|[[Project Knowledge sharing]]<br />
|-<br />
|Augustin<br />
|Bouet<br />
|s142823<br />
|[[Metra Potential Method]]</div>S113440http://13.50.150.85/index.php?title=Fault_tree_analysis&diff=7648Fault tree analysis2015-09-09T16:36:01Z<p>S113440: Created page with "'''Fault Tree Analysis''' Blablabla = Big Idea = = Applications = = Limitations = = Annotated Bibliography = = Sample Code snips = This is a list *List1 *List2 *List2 T..."</p>
<hr />
<div>'''Fault Tree Analysis'''<br />
<br />
Blablabla<br />
<br />
<br />
<br />
<br />
= Big Idea =<br />
= Applications =<br />
= Limitations =<br />
= Annotated Bibliography =<br />
= Sample Code snips =<br />
<br />
This is a list<br />
*List1<br />
*List2<br />
*List2<br />
<br />
This is a picture<br />
[[File:Fig_1_Process.jpg|600px|thumb|left|Figure 1: Process for Individual Assignment]]<br />
<br />
This is big, italian and underlined<br />
<u>* '''You can choose to work on one of two types of articles:''' *</u><br />
<br />
Here's some links<br />
<br />
[[Articles Fall Term 2015]]<br />
[//meta.wikimedia.org/wiki/Help:Contents User's Guide]<br />
[//www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
[//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
[https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]<br />
[http://www.mediawiki.org/wiki/Help:Contents Help Content]<br />
<br />
Aaanndd some references<br />
<br />
*References Cite link: [http://www.mediawiki.org/wiki/Extension:Cite Cite]<br />
**To create a reference link in the text like this <ref>[http://www.facstaff.bucknell.edu/ttoole/Toole%20PM%20Causal%20Loop%20Diagram.pdf A project management causal loop diagram, Toole, Michael, 2005.] </ref> write <nowiki><ref>[''link/title''] ''Name of link'' </ref></nowiki><br />
** Create a reference list like this one, by writing <nowiki><references /></nowiki> <references /></div>S113440