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An Introduction to Fault TreeAnalysis (FTA)
Dr Jane Marshall
Product Excellence using 6 SigmaModule
PEUSS 2011/2012 FTA Page 1
Objectives
– Understand purpose of FTA
– Understand & apply rules of FTA
– Analyse a simple system using FTA
– Understand & apply rules of Boolean algebra
PEUSS 2011/2012 FTA Page 2
2
Relationship between FMEA& FTA
Part Failure
Product Failure
Failure Mode & EffectAnalysis (FMEA)
Fault TreeAnalysis (FTA)
PEUSS 2011/2012 FTA Page 3
Fault Tree Analysis
• Is a systematic method of System Analysis
• Examines System from Top Down
• Provides graphical symbols for ease of understanding
• Incorporates mathematical tools to focus on critical areas
PEUSS 2011/2012 FTA Page 4
3
Fault tree analysis (FTA)
• Key elements:
– Gates represent the outcome
– Events represent input to the gates
• FTA is used to:
– investigate potential faults;
– its modes and causes;– and to quantify their contribution to system unreliability in the
course of product design .
PEUSS 2011/2012 FTA Page 5
Symbols
A B
‘AND’ Gate
A B
‘OR’ Gate
Basic Event
Transfer in
Transfer out
PEUSS 2011/2012 FTA Page 6
A U BA ∩ B
4
Example Fault Tree
54 65
64
54 65
64
64 531 2
97 8
1 2
109
7 8
•A
21 32
31
21 32
31
•A
Top eventA developed Tree …..
… .. Ready for analysis
PEUSS 2011/2012 FTA 7
Example: redundant fire pumps
Source: http://www.ntnu.no/ross/srt/slides/fta.pdf
PEUSS 2011/2012 FTA Page 8
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Example: redundant fire pumps
Source: http://www.ntnu.no/ross/srt/slides/fta.pdf
PEUSS 2011/2012 FTA Page 9
Example
PEUSS 2011/2012 FTA Page 10
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Example
PEUSS 2011/2012 FTA Page 11
Methodology (PreliminaryAnalysis)
• Set System Boundaries
• Understand Chosen System
• Define Top Events
PEUSS 2011/2012 FTA Page 12
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1. The “Immediate, Necessary & Sufficient” Rule
2. The “Clear Statement” Rule
3. The “No Miracles” Rule
4. The “Complete-the-Gate” Rule
5. The “No Gate-to-Gate” Rule
6. The “Component or System Fault?” Rule
Methodology (Rules)
PEUSS 2011/2012 FTA Page 13
Closest in space, time and derivation of the event above
Necessary
There is no redundancy in the statement or gate linkageThe event above could not result from a sub set of the causaleventsSufficient
The events will, in all circumstances and at all times, causethe event above
Methodology (Rules - 1) –immediate, necessary and sufficientcause
Immediate
PEUSS 2011/2012 FTA Page 14
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Write event box statements clearly, statingprecisely what the event is and when itoccurs
Methodology (Rules - 2) – Theclear statement rule
PEUSS 2011/2012 FTA Page 15
If the answer to the question:
“Can this fault consist of a component failure?” is Yes,
– Classify the event as a “State of component fault”
If the answer is No,
– Classify the event as a “state of system fault”
Methodology (Rules - 3) – The‘component or systems fault’ rule
PEUSS 2011/2012 FTA Page 16
9
If the normal functioning of a componentpropagates a fault sequence, then it isassumed that the component functionsnormally
Methodology (Rules - 4) – nomiracles rule
PEUSS 2011/2012 FTA Page 17
All inputs to a particular gate should becompletely defined before furtheranalysis of any one of them isundertaken
Methodology (Rules - 5) – thecomplete gate rule
PEUSS 2011/2012 FTA Page 18
10
Gate inputs should be properly defined faultevents, and gates should not be directlyconnected to other gates
Methodology (Rules - 6) no gateto gate rule
PEUSS 2011/2012 FTA Page 19
Battery
Switch
Motor
Connector A
Connector B….. Motor does notrun when switch ispressed
Fault Tree Example
PEUSS 2011/2012 FTA Page 20
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Fault Tree Example
Motor does notrun
No PowerSupplyMotor
failed
Noconnection
Switchmalfunction Battery
is dead
ConnectorB
detached
Connector
detachedAInsufficient
force isapplied
Switchis
broken
top event …..
motor does not runwhen switch is pressed
PEUSS 2011/2012 FTA Page 21
Algebraic representation is:Q = ( A C ) ( D B )
or gate and gate
Qualitative Analysis(Combination of Gates)
PEUSS 2011/2012 FTA Page 22
Q
A C D B
12
Qualitative Analysis(Cut Sets)
A listing taken directly from the Fault Treeof the events, ALL of which must occur tocause the TOP Event to happen
PEUSS 2011/2012 FTA Page 23
Algebraic representation is:
Q = ( A C ) ( D B )
which can be re-written as:
Q = ( A D ) ( A B ) ( C D ) ( C B )Q = ( A • D ) + ( A • B ) + ( C • D ) + ( C • B )
… which is a listing of Groupings ...each ofwhich is a Cut Set
AD AB CD BC
Qualitative Analysis (Cut Sets)
PEUSS 2011/2012 FTA Page 24
Q
A C D B
13
Qualitative Analysis(Minimal Cut Sets)
A listing, derived from the Fault Tree Cut Sets andreduced by Boolean Algebra, which is the smallestlist of events that is necessary to cause the TopEvent to happen
PEUSS 2011/2012 FTA Page 25
Qualitative Analysis(Boolean Algebra)
Commutative lawsA B = B AA B = B A
Associative lawsA (B C) = (A B) CA (B C) = (A B) C
Distributive lawsA (B C) = A B A CA (B C) = (A B) (A C)
PEUSS 2011/2012 FTA Page 26
Commutative lawsA • B = B • AA + B = B +A
Associative lawsA • (B • C) = (A • B) • CA + (B + C) = (A + B) + C
Distributive lawsA • (B + C) = A • B + A • CA + (B • C) = (A + B) • (A + C)
14
Qualitative Analysis(Boolean Reduction)
Idempotent laws
A • A = AA +A = A
Absorption law
A + (A • B) = A
Top event
AB
A
PEUSS 2011/2012 FTA Page 27
CA BD
CDBA
A B D C
A C D B
( A C ) ( D B )
( A B ) ( ( A C ) ( D B ) ) ( D C )
Exercise in deriving Cut Sets…..
PEUSS 2011/2012 FTA Page 28
15
Solution …..
( A B ) (( A C ) ( D B )) ( D C )
( A + B ) • ( A • C + D • B ) • D • C
AACDC + ADBDC + BACDC + BDBDC
ACD + ABCD + ABCD + BCD
ACD + BCD
Minimal Cut Sets …… ACD, BCD
PEUSS 2011/2012 FTA Page 29
Design Analysis of Minimal Cut Sets
A Cut Set comprising several components is less likely to fail thanone containing a single component
Hint .....
AND Gates at the top of the Fault Tree increase the number ofcomponents in a Cut Set
OR Gates increase the number of Cut Sets, but often lead to singlecomponent Sets
PEUSS 2011/2012 FTA Page 30
16
Benefits and limitations
• Prepared in early stages of a design and further developed indetail concurrently with design development.
• Identifies and records systematically the logical fault paths from aspecific effect, to the prime causes
• Allows easy conversion to probability measures
• But may lead to very large trees if the analysis is extended indepth.
PEUSS 2011/2012 FTA Page 31
• Depends on skill of analyst
• Difficult to apply to systems with partial success
• Can be costly in time & effort
Software
• Software packages available for reliability tools
• Relex
• Relia soft
• others
PEUSS 2011/2012 FTA Page 32
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Exercise 1
PEUSS 2011/2012 FTA Page 33
OnePossibleSolution
PEUSS 2011/2012 FTA Page 34
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RBD of an engine
PEUSS 2011/2012 FTA Page 35
Ignition system 2
Ignition system 1
CarburettorFuel system
Fuelpump
Fuelfilter Jet
Othercomponents
LV HV
LV HV
PEUSS 2011/2012 FTA Page 36
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