Fault tree analysis - Revision history

Tkokotas at 15:35, 18 December 2018

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			''Developed by Jacob Gjerstrup''


	'''Fault Tree Analysis'''		'''Fault Tree Analysis'''

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	= Applications =		= Applications =
			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.
	==Basic fault trees==		==Basic fault trees==
	[[File:SymbolsOfFaultTrees.png\|300px\|thumb\|right\|Figure 2: The basic figures of a fault tree]]		[[File:SymbolsOfFaultTrees.png\|300px\|thumb\|right\|Figure 2: The basic figures of a fault tree]]

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	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.		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.

	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.		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.

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	'''Fault Tree Analysis'''		'''Fault Tree Analysis'''

	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.		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.
	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.		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.

	~~This article will consist of four sections:~~

	*'''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.
	*'''Applications:''' This section will explain how to use FTA.
	*'''Limitations:''' This section will explore the limitations of FTA.
	*'''Annotated Bibliography:''' This section will provide key references that can be read for further elaboration on FTA.

	= Big Idea =		= Big Idea =

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	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>		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>




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	'''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>		'''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>

	'''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>		'''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>

	'''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>		'''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>
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	=Conclusion=		=Conclusion=
	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.		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.

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	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.		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.

	~~<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.		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.

	~~<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.		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.

	~~<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		http://www.weibull.com/hotwire/issue63/relbasics63.htm :Provides a more in-depth description of what a minimal cut set is



	<references/>		<references/>

S113440 at 20:48, 28 September 2015

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	= Annotated Bibliography =		= Annotated Bibliography =
	[[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.		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.

	<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.		<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.

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	= Annotated Bibliography =		= Annotated Bibliography =
	~~<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.		[[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.

	<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.		<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.

S113440 at 20:47, 28 September 2015

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	= Annotated Bibliography =		= Annotated Bibliography =
	[[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.		<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.

			<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.

	[[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~~.		<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.

			<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
	[[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.~~


	[[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]: Provides a more in-depth description of what a minimal cut set is



	<references/>		<references/>

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	= Big Idea =		= Big Idea =
			==History==
			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>.

	==Concept and purpose==		==Concept and purpose==
	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.		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.
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	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>		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>

	~~==History==~~
	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>.


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	[[File:Minimumcutset.png\|300px\|thumb\|right\|Figure 3: Minimal cut set example]]		[[File:Minimumcutset.png\|300px\|thumb\|right\|Figure 3: Minimal cut set example]]

	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>		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>

	==Advanced Fault trees==		==Advanced Fault trees==
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	'''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>		'''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>

			=Conclusion=
			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.


	= Annotated Bibliography =		= Annotated Bibliography =
			[[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.


			[[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.


			[[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.


			[[http://www.weibull.com/hotwire/issue63/relbasics63.htm]]: Provides a more in-depth description of what a minimal cut set is



	<references/>		<references/>