1. What is Fault Tree Analysis?
Fault Tree Analysis(FTA) is one of the several deductive logic model techniques, and one of the most common hazard identification tool.
The deduction begins with a stated top level hazardous/undesired event.
It uses logic diagrams and Boolean Algebra to identify single events and combinations of events that could cause the top event.
Probability of occurrence values are assigned to the lowest events in the tree in order to obtain the probability of occurrence of the top event.
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2. Fault tree main symbols.
Commonly Used Symbols Occasionally Used Symbols
OR gate Incomplete event
AND gate An External Event
An Event / Fault Inhibit gate
Basic Event
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3. FTA Symbols Explained
Basic Event: A lower most event that can not be further developed. E.g. Relay failure, Switch failure etc.,
An Event / Fault: This can be a intermediate event (or) a top event. They are a result logical combination of lower level events. E.g. Both transmitters fail, Run away reaction
OR Gate: Either one of the bottom event results in occurrence of the top event E.g. Either one of the root valve is closed, process signal to transmitter fails.
AND Gate: For the top event to occur all the bottom events should occur E.g. Fuel, Oxygen and Ignition source has to be present for fire.
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4. FTA Symbols Explained
Incomplete Event: An event which has scope for further development but not done usually because of insufficient data. E.g. Software malfunction, Human Error etc.,
External Event: An event external to the system which can cause failure. E.g. Fire.
Inhibit Gate: The top event occurs only if the bottom event occurs and the inhibit condition is true E.g. False trip of unit on “maintenance override” not ON.
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5. Simple Examples OR AND Example 1: Example 2: 0.28 Transmitter Failed
0.1
0.2
(2E-06)
Valve Failed
AND
Valve 1
Failed
Valve 2
Failed
0.001
0.002
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6. Procedure 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
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7. Procedure Define Top Event:
Use PHA, P&ID, Process description etc., to define the top event.
If its too broad, overly large FTA will result. E.g. Fire in process.
If its too narrow, the exercise will be costly. E.g. Leak in the valve.
The boundaries for top event definition can be a System, Sub-system, Unit, Equipment (or) a Function.
Some good examples are: Overpressure in vessel V1, Motor fails to start, Reactor high temperature safety function fails etc.,
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8. Procedure Procedure for Fault Tree Analysis Define TOP event
Define overall
structure.
Explore each
branch in
successive level
of detail.
Perform
corrections if
required and
make decisions
Solve the fault
tree
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9. Procedure Define overall structure:
Determine the intermediate events & combination of failure that will lead to the top event.
Arrange them accordingly using logical relationship.
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10. Procedure Procedure for Fault Tree Analysis: Define TOP event
Define overall
structure.
Explore each
branch in
successive level
of detail.
Perform
corrections if
required and
make decisions
Solve the fault
tree
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11. Procedure Explore each branch in successive level of detail:
Continue the top down process until the root cause for each branch is identified and/or until further decomposition is considered unnecessary.
So each branch will end with a basic event or an undeveloped event.
Consider Common cause failure & Systematic failures in the process of decomposition.
A good guide to stop decomposing is to go no further than physical (or) functional bounds set by the top event.
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12. Procedure Procedure for Fault Tree Analysis: Define TOP event
Define overall
structure.
Explore each
branch in
successive level
of detail.
Perform
corrections if
required and
make decisions
Solve the fault
tree
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13. Procedure Solve the Fault Tree:
Assign probabilities of failure to the lowest level event in each branch of the tree.
From this data the intermediate event frequency and the top level event frequency can be determined using Boolean Algebra and Minimal Cut Set methods.
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14. Procedure Steps to get the final Boolean equation:
1. Replace AND gates with the product of their inputs.
IE1 = A.B
IE2 = C.D
2. Replace OR gates with the sum of their inputs.
TOP = IE1+IE2
= A.B+C.D
3. Continue this replacement until all intermediate event gates
have been replaced and only the basic events remain in the
equation.
TOP = A.B+C.D
TOP
IE1
IE2 A B C D
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15. Procedure Minimal Cut Set theory:
The fault tree consists of many levels of basic and intermediate events linked together by AND and OR gates. Some basic events may appear in different places of the fault tree.
The minimal cut set analysis provides a new fault tree, logically equivalent to the original, with an OR gate beneath the top event, whose inputs (bottom)are minimal cut sets.
Each minimal cut set is an AND gate with a set of basic event inputs necessary and sufficient to cause the top event.
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16. Procedure Boolean Algebra Reduction Example: TOP = IE1 + IE2
= (A.B) + (A + IE3)
= A.B + A + (C.D.IE4)
= A.B + A + (C.D.D.B)
= A + A.B + B.C.D.D (D.D = D)
= A + A.B + B.C.D (A + A.B = A)
= A + B.C.D
So the minimal cut sets are:
CS1 = A
CS2 = B.C.D
meaning TOP event occurs if
either A occurs OR (B.C.D) occurs. A B
IE3 C D
IE4
TOP
IE1
IE2
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17. Procedure Procedure for fault tree analysis: Define TOP event
Define overall
structure.
Explore each
branch in
successive level
of detail.
Perform
corrections if
required and
make decisions
Solve the fault
tree
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18. Procedure Perform corrections and make decisions:
Application of Boolean Algebra and Minimal Cut Set theory will result in identifying the basic events(A) and combination of basic events(B.C.D) that have major influence on the TOP event.
This will give clear insight on what needs to be attended and where resources has to be put for problem solving.
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19. Advantages of FTA Plus points of FTA:
Deals well with parallel, redundant or alternative fault paths.
Searches for possible causes of an end effect which may not have been foreseen.
The cut sets derived in FTA can give enormous insight into various ways top event occurs.
Very useful tool for focused analysis where analysis is required for one or two major outcomes.
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20. Disadvantages of FTA Minus points of FTA:
Requires a separate fault tree for each top event and makes it difficult to analyze complex systems.
Fault trees developed by different individuals are usually different in structure, producing different cut set elements and results.
The same event may appear in different parts of the tree, leading to some initial confusion.
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21. END
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