fault tree analysis

 Fault Tree Analysis (FTA) is one of the most
important logic and probabilistic techniques
used in Probabilistic Risk Assessment (PRA)
and system reliability assessment.
 Fault Tree Analysis (FTA) attempts to model
and analyze failure processes of engineering
systems. FTA can be simply described as an
analytical technique

FTA is a deductive analysis approach for
resolving an undesired event into its causes.
Logic diagrams and Boolean Algebra are used
to identify the cause of the top event.

 Fault tree is the logical model of the relationship
of the undesired event to more basic events.
 The top event of the Fault tree is the undesired
event.
 The middle events are intermediate events and
the basic events are at the bottom.
 The logic relationship of events are shown by
logic symbols or gates.

 A primary fault is any fault of a component that occurs in
an environment for which the component is qualified e.g.,
a pressure tank, designed to withstand pressures up to and
including a pressure Po, ruptures at some pressure p <Po
because of a defective weld.
 A secondary fault is any fault of a component that occurs
in an environment for which it has not been qualified. In
other words, the component fails in a situation which
exceeds the conditions for which it was designed; e.g., a
pressure tank, designed to withstand pressure up to and
including a pressure Po, ruptures under a pressure p > PO.
 Because primary and secondary faults are generally
component failures, they are usually called primary and
secondary failures. A command fault in contrast, involves
the proper operation of a component but at the wrong
time or in the wrong place;

Basic Event: A lower most event that can not be further
developed.
Intermediate Event: This can be a intermediate
event (or) a top event. They are a result logical combination
of lower level events.
Undeveloped Event: An event which has
scope for further development but not done
usually because of insufficient data.
External Event: An event external to the
system which can cause failure.

OR Gate: Either one of the bottom event
results in the occurrence of the top event.
AND Gate: For the top event to occur all the
bottom events should occur.
Inhibit Gate: The top event occurs
only if the bottom event occurs and
the inhibit condition is true.

Procedure for Fault Tree Analysis
Define TOP
event
Define overall
structure.
Explore each
branch in
successive level
of detail.
Solve the fault
tree
Perform
corrections if
required and
make decisions

 1. Define the undesired event to be
analyzed (the focus of the FTA)
 2. Define the boundary of the system (the
scope of the FTA)
 3. Define the basic causal events to be
considered (the resolution of the FTA)
 4. Define the initial state of the system

 • Undesired top event: Motor does not start
when switch is closed
 • Boundary of the FT: The circuit
containing the motor, battery, and switch
 • Resolution of the FT: The basic
components in the circuit excluding the
wiring
 • Initial State of System: Switch open,
normal operating conditions

 • The top event should describe WHAT the
event is and WHEN it happens
 • The top event is often a system failure
but can be any other event
 • The top event is the specific event to be
resolved into its basic causes
 • Defining the wrong top event will result in
wrong assessments and conclusions

 1. Define the top event as a rectangle
 2. Determine the immediate necessary and
sufficient events which result in the top event
 3. Draw the appropriate gate to describe the logic
for the intermediate events resulting in the top
event
 4. Treat each intermediate event as an
intermediate level top event
 5. Determine the immediate, necessary and
sufficient causes for each intermediate event
 6. Determine the appropriate gate and continue
the process

 The system being analyzed for the
undesired event needs to be studied and
understood before the fault tree is
constructed
 If an electrical or hydraulic system is being
analyzed, the fault tree is constructed by
tracing the causes upstream in the circuit
to the basic causes
 For a generalized network or flow, the
fault tree is similarly constructed by
upstream tracing of the causes

 Top Event- What specific event is being analyzed?
 Boundary- What is inside and outside the analysis?
 Resolution- What are the primary causes to be
resolved to?
 Initial State- What is assumed for the initial conditions
and states?

 Do not assume abnormal conditions will
occur to prevent a fault from propagating
 In particular, do not assume a failure of
another component will occur to prevent a
fault from propagating

 Each Gate and Event on the Fault Tree
needs to be named
 The Name should ideally identify the Event
Fault and the What and When Conditions
 Basic events should in particular be named
to identify the failure mode
 What is important is that the same event
be given the same name if it appears at
different locations

 Human errors are classified into two basic types-errors
of omission and errors of commission
 An error of omission is not doing a correct action
 An error of commission is doing an incorrect action
 Human errors are modeled as basic events in a FT,
similarly to component failures
 Human errors need to be considered whenever a
human interfaces with the component or system
 The failure modes need to be expanded to include
failure induced by the human

 Test and maintenance related errors
 Errors causing initiating events
 Procedural errors during an incident or
accident
 Errors leading to inappropriate actions
 Detection and Recovery errors

• The system operates in different phases
• The system configuration can change in different
phases
• The system success criteria can change
• The basic event probabilities (e.g, component failure
rates) can change

 For each phase there are distinct basic event
probabilities but no system logic changes
 Each basic event is thus resolved into individual
phase events

 Changes in event probabilities can alternatively be
handled in the quantification stage

 A minimal cutset (mcs) is a smallest combination of
primary events, or basic events, causing the top
event
 All the primary events need to occur to cause the
top event
 Each mcs is thus a causal-combination, i.e., a
combination of primary events
 The complete set of mcs provides the complete set
of causes of the top event

 The fault tree is represented as a set of logic equations
 Substitution is carried out until the top event is
 represented entirely in terms of basic events
 The top event equation is then expanded and
simplified to obtain a ‘sum of products’
 In expanding the top event equation, the Boolean
distributive law and the law of absorption are used
 Each product in the sum of products is then a
minimal cut set of the top event

 A•(B + C) = A•B + A•C Distributive Law
 A + A = A Identity Union Law
(Identity Absorption Law)
 A + A•B = A Subset Absorption Law
 A•A = A Identity Intersection Law
(Idempotent Law)
 (A + B)’= A’•B’ Union Complementation Law
 (A•B)’= A’ + B’ Intersection Complementation

Applying the Distributive Law and Laws of Absorption to the Top
Event Equation in terms of the Basic Events
Q =C1 OR C2
C1=B1 OR B2
C2= B2 oR B3
Q =(B1+B2) •(B2+B3)
Q =(B1 •B2)+(B1•B3)+(B2•B2)+(B2•B3)
Q =(B1 •B2)+(B1•B3)+B2+(B2•B3)

Failure probability for a non-repairable
component (or event)
P = 1-exp(-λT) ~ λT λ = component failure rate
T = exposure time
Failure probability for a repairable component
P = λτ/(1+ λτ) ~ λτ τ = repair time
Constant failure probability for a component
P = c c = constant probability

 1. Identify the specific component failure mode
 2. Determine whether the failure is time-related or
demand related
 3. Determine the environment e.g., ground or air
 4. Select the appropriate failure rate value
 5. For a time-related failure determine the exposure
time
 6. For a time-related failure, if the failure is repairable
determine the repair time
 7. For a demand-related failure, determine the number of
demands if greater than 1

 FV Importance (Contribution Importance)- the
relative contribution to the top event
probability from an event.
 Risk Achievement Worth RAW (Increase
Sensitivity,Birnbaum Importance)- the increase
in the top event probability when an event is
given to occur
 Risk Reduction Worth RRW (Reduction
Sensitivity)- the reduction in the probability of
the top event when an event is given to not
occur

 FV Importance = Sum of min cut cuts containing the event
Sum of all min cut sets
RAW =Top event probability with event probability set to 1
RRW = Top event probability with event probability set to 0

A Success Tree (ST) identifies all the ways in
which the top event cannot occur
 The ST is the complement of the FT
 The ST is the mirror of the FT
The ST is useful in showing the explicit ways to
prevent the occurrence of the FT

 Complement the top event to a NOT event
 Complement all intermediate events to NOT
Events
 Complement all basic events to NOT events
 Change all AND gates to OR gates
 Change all OR gates to AND gates
 The minimal cut sets of the ST are now called the
minimal path sets

 A minimal path set is the smallest number of
events which if they all do not occur then the
top event will not occur
 If the events in one path set are prevented to
occur then the top event will be guaranteed
to not occur
 The minimal path sets are the totality of
ways to prevent the top event based on the
fault tree

 Define the FTA
– Top Event
– Scope
– Resolution
 Assemble the project Team
– FT analyst
– System engineering support
– Data support
– Software support
 Define the FTA Operational Framework
– Assemble the as built drawings
– FT naming scheme
– Interfaces/Support to be modeled
– Software to be used

 Assemble the data
– Generically applicable data
– Specifically applicable data
 Prepare the software package
– Familiarization
– Test problems
 Keep a log on the FTA work
– Operational and design assumptions
– Events not modeled and why
– Success and failure definitions
– Special models and quantifications used

 Review the work at stages
– FT construction
– Qualitative evaluations
– Quantitative evaluations
 Check and validate the results
– Engineering logic checks
– Consistency checks with experience
 Prepare and disseminate the draft report
– Conclusions/findings
– FTA results
– FTs
– Software inputs/outputs
 Obtain feedback and modify and final report
– Disseminate the report
– Present findings

 1) “Fault Tree Handbook with Aerospace Applications’
Version 1.1, NASA Publication, August 2002
 2) Fault Tree Analysis (FTA) ,Concepts and Applications
Bill Vesely,NASA HQ
3)Tutorial fault tree analysis
Dr John Andrews,1998
3) Fault tree analysis,4ᵀᴴEdition P.L.Clemens1993
4) Fault tree analysis,Clifton A.Ericson II
 5) Fault Tree Handbook with Aerospace Applications
 Version 1.1, Prepared for NASA Office of Safety and
Mission Assurance, NASA Headquarters
Washington DC 20546 , August 2002

fault tree analysis

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fault tree analysis