An Introduction to Fault Tree Analysis (FTA) Objectives

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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


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Relationship between FMEA& FTA

Part Failure

Product Failure

Failure Mode & EffectAnalysis (FMEA)

Fault TreeAnalysis (FTA)


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


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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 .


Symbols

A B

‘AND’ Gate

A B

‘OR’ Gate

Basic Event

Transfer in

Transfer out


A U BA ∩ B

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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


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Example: redundant fire pumps

Source: http://www.ntnu.no/ross/srt/slides/fta.pdf


Example


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Example


Methodology (PreliminaryAnalysis)

• Set System Boundaries

• Understand Chosen System

• Define Top Events


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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)


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


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Write event box statements clearly, statingprecisely what the event is and when itoccurs

Methodology (Rules - 2) – Theclear statement rule


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


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If the normal functioning of a componentpropagates a fault sequence, then it isassumed that the component functionsnormally

Methodology (Rules - 4) – nomiracles rule


All inputs to a particular gate should becompletely defined before furtheranalysis of any one of them isundertaken

Methodology (Rules - 5) – thecomplete gate rule


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Gate inputs should be properly defined faultevents, and gates should not be directlyconnected to other gates

Methodology (Rules - 6) no gateto gate rule


Battery

Switch

Motor

Connector A

Connector B….. Motor does notrun when switch ispressed

Fault Tree Example


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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


Algebraic representation is:Q = ( A C ) ( D B )

or gate and gate

Qualitative Analysis(Combination of Gates)


Q

A C D B

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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


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)


Q

A C D B

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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


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)


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)

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Qualitative Analysis(Boolean Reduction)

Idempotent laws

A • A = AA +A = A

Absorption law

A + (A • B) = A

Top event

AB

A


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…..


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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


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


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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.


• 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


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Exercise 1


OnePossibleSolution


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RBD of an engine


Ignition system 2

Ignition system 1

CarburettorFuel system

Fuelpump

Fuelfilter Jet

Othercomponents

LV HV

LV HV


Documents

An Introduction to Fault Tree Analysis (FTA) Objectives