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FAULT & EVENT TREE ANALYSIS
BY
NITESH M. DONGARE
FAULT TREE ANALYSIS
DEFINITION
• 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 Trees are deductive method for identifying ways in which hazards can lead to accident.
• The approach starts with a well defined accident ,or top event, and works backwards towards the various scenarios that can cause the accident.
STEPS IN CARRYING OUT A FAULT TREE ANALYSIS
1. Identify the objective for the FTA.
2. Define the top event of the FT.
3. Define the scope of the FTA.
4. Define the resolution of the FTA.
5. Define ground rules for the FTA.
* The first five steps involve the problem formulation for an FTA.
6. Construct the FT.
7. Evaluate the FT.
8. Interpret and present the results.
• The remaining steps involve the actual construction of the FT, the evaluation of the FT, and the interpretation of the FT results.
SYMBOL REPRESENTATIONS
Circle – it means that basic failure
Diamond – it means that basic fault
Rectangle – it means that resultant event
Double diamond – represents an event
House – represents the basic event
FAULT TREE CONSTRUCTION`
Consider the following block diagram. Let I/P and O/P be the inputAnd output terminals. There are two sub-systems A and B that are connected in series.
INPUT OUTPUTX 1 X 3
X 2 X 4
SUB - SYSTEM (A) SUB - SYSTEM (B)
For this the fault tree analysis diagram shown in next slide
F (S)
AND
F (A) F (B)
OR
F( X 1) F( X 3)F( X 2) F( X 4)
AND
Top event
intermediate event
Basic event
CONTINUE…..Here F(x1) , F(x2) , F(x3), F(x4) Are Events Fail…
F (A) = SUB – SYSTEM (A) FAILS
F(B) = SUB – SYSTEM (B) FAILS
THEN F(A) = F(X1) AND F(X2)
AND F(B) = F(X3) AND F(X4)
FINALLY THE FAILURE OF THE SYSTEM
F(S) = F(A) OR F(B)
CALCULATION OF RELIABILITYFROM FAULT TREE
CONSIDER THE EARLIER BLOCK DIAGRAM
The probability of failure of sub – system (A) is indicated as shown in below,
P(A) = P (X 1 and X 2)
P(A) = P( X1) * P( X 2)
Similarly for sub – system (B)
P(B) = P( X 3 and X 4)
P(B) = P( X 3) * P( X 4)
FAILURE OCCURS WHEN SUB – SYSTEM (A) or (B) FAIL..,
F (S) = P(A) or P(B) THEN F(S) = P(A) + P(B) – ( P(A) * P(B) )
IF THE RELIABILITY OF THE ELEMENTS ARE GIVEN BY R1,R2,R3,R4
THENP( Xi ) = 1 – Ri
RELIABILITY OF SYSTEM R(S) = 1 - F(S)
1. For an emergency operation theatre in a hospital, the power is obtained from the main city supply through a transformer connected in series. To ensure an uninterrupted supply, an auxiliary generator is also used with a suitable switch-over. The probability of failure of the city supply is 0.01 and the transformer reliability is 0.996. the auxiliary power generator has a reliability factor of 0.99. draw the block diagram for the system. Construct the fault tree and, based on this, calculate the reliability of the system.
mains
transformer
generator
Operation
theatre
BLOCK DIAGRAM
X 1 X 2
X 3
INPUT
OUTPUT
Fault tree for problem
F (S)
AND
OR
A B C
Main fails Transformer fails
Generator fails
SOLUTIONFAILURE OF THE SYSTEM
F (S) = ( P ( X1 ) or P(X 2) ) and P( X 3 )
P ( X 1) = 0.01
P ( X 2) = 1 – 0.996 = 0.004
P ( X 3) = 1 – 0.99 = 0.001
F (S) = ( P (X 1) + P (X 2 ) – ( P (X1 ) * P(X2) ) ) * ( P (X 3 ) ) = ( 0.01 + 0.004 – ( 0.01 * 0.004) ) * (0.001)
F(S) = 0.0001396
FOR RELIABILITYR(S) = 1- F(S)
= 1- 0.0001396
R(S) = 0.99986
USES
• Use of FTA to understand of the logic leading to the top event.
• Use of FTA to prioritize the contributors leading to the top event.
• Use of FTA as a proactive tool to prevent the top event.
• Use of FTA to monitor the performance of the system.
• Use of FTA to minimize and optimize resources.
• Use of FTA to assist in designing a system.
• Use of FTA as a diagnostic tool to identify and correct causes of the top event.
ADVANTAGES
• Begins with top event.
• Use to determine the minimal cut sets.
DISADVANTAGES
• Complicated process.
• Require considerable amount of time to complete.
EVENT TREE ANALYSIS
DEFINITION
• Event trees begin with an initiating event & work towards the final result.
• This method provides information on how a failure can occur & the probability of occurrence.
STEPS INVOLVED IN AN ETA
1. Identify an initiating event of interest.
2. Identify the safety functions designed
to deal with the initiating event.
3. Construct the event tree.
4. Describe the resulting accident event sequences
EXAMPLE
• Oxidation reactor high temp. Alarm alerts operator at temp T1.
• Operator reestablish cooling water flow to the oxidation reactor.
• Automatic shutdown system stops reaction at temp. T2. ( T2 > T1)
These safety functions are listed in the order in which they are intended to occur.
Reactor
TIA
TIC
Alarmat
T > TA
Cooling Coils
Thermocouple
High Temperature Alarm
TemperatureController
Reactor Feed
Cooling Water Out
Cooling Water In
Figure 11-8 Reactor with high temperature alarm and temperature controller.
Step 1 - Identify the initiating event
• system or equipment failure
• human error
• process upset
[Example] “Loss of Cooling Water” to an Oxidation Reactor
Step 2 - Identify the Safety Functions Designed to Deal with the Initiating Event
• Safety system that automatically respond to the initiating event.
• Alarms that alert the operator when the initiating event occurs and operator actions designed to be performed in response to alarms or required by procedures.
• Barriers or Containment methods that are intended to limit the effects of the initiating event.
Step 3: Construct the Event Tree a. Enter the initiating event and safety functions.
SAFETYFUNCTION
Oxidation reactorhigh temperature
alarm alerts operator
at temperature T1
Operatorreestablishes
cooling water flowto oxidation
reactor
Automaticshutdown systemstops reaction attemperature T2
INITIATING EVENT:
Loss of cooling waterto oxidation reactor
FIRST STEP IN CONSTRUCTING EVENT TREE
SAFETYFUNCTION
Oxidation reactorhigh temperature
alarm alerts operator
at temperature T1
Operatorreestablishes
cooling water flowto oxidation
reactor
Automaticshutdown systemstops reaction attemperature T2
INITIATING EVENT:
Loss of cooling waterto oxidation reactor
Success
Failure
REPRESENTATION OF THE FIRST SAFETY FUNCTION
Step 3: Construct the Event Tree b. Evaluate the safety functions
Step 3: Construct the Event Tree b. Evaluate the safety functions
SAFETYFUNCTION
Oxidation reactorhigh temperature
alarm alerts operator
at temperature T1
Operatorreestablishes
cooling water flowto oxidation
reactor
Automaticshutdown systemstops reaction attemperature T2
INITIATING EVENT:
Loss of cooling waterto oxidation reactor
Success
Failure
If the safety function does not affect the course of the accident, the accident path proceeds with no branch pt to the next safety function.
REPRESENTATION OF THE SECOND SAFETY FUNCTION
Step 3: b. Evaluate safety functions.
SAFETYFUNCTION
Oxidation reactorhigh temperature
alarm alerts operator
at temperature T1
Operatorreestablishes
cooling water flowto oxidation
reactor
Automaticshutdown systemstops reaction attemperature T2
INITIATING EVENT:
Loss of cooling waterto oxidation reactor
COMPLETED EVENT TREE
Success
Failure
Completed !
Step 4: Describe the Accident Sequence
SAFETYFUNCTION
Oxidation reactorhigh temperature
alarm alerts operator
at temperature T1
Operatorreestablishes
cooling water flowto oxidation
reactor
Automaticshutdown systemstops reaction attemperature T2
INITIATING EVENT:
Loss of cooling waterto oxidation reactor
ACCIDENT SEQUENCES
Success
Failure
Safe condition,return to normaloperation
Safe condition,process shutdown
Unsafe condition,runaway reaction,operator aware ofproblem
Unstable condition,process shutdown
Unsafe condition,runaway reaction,operator unaware of problem
B
A
C DA
AC
ACD
AB
ABD
Safety Function:
Identifier: B C D E
Failures/Demand: 0.01 0.25 0.25 0.1
High TempAlarm Alerts
Operator
OperatorNotices
High Temp
OperatorRe-startsCooling
OperatorShuts Down
Reactor Result
Shutdown = 0.2227 + 0.001688 + 0.005625 = 0.2250 occurrences/yr.
Runaway = 0.02475 + 0.0001875 + 0.0000625 = 0.02500 occurrences/yr.
Figure 11-9 Event tree for a loss of coolant accident for the reactor of Figure 11-8.
Initiating Event:
Loss of Cooling
1 Occurrence/yr.
A
1
A0.7425AD0.2227ADE0.02475AB0.005625ABD0.001688ABDE0.0001875ABC0.001875ABCD0.0005625ABCDE0.0000625
0.99
0.01
0.2475
0.001875
0.000625
0.0075
0.0025
Continue Operation
Shut Down
Runaway
Continue Operation
Shut Down
Runaway
Continue Operation
Shut Down
Runaway
Safety Function0.01 Failures/Demand
InitiatingEvent
0.5 Occurrences/yr.
Success of Safety Function
(1-0.01)*0.5 = 0.495 Occurrence/yr.
Failure of Safety Function
0.01*0.5 = 0.005 Occurrence/yr.
Figure 11-10 The computational sequence across a safety function in an event tree.
Safety Function:
Identifier: B C D E FFailures/Demand: 0.01 0.25 0.25 0.01 0.1
High TempAlarm Alerts
Operator
OperatorNotices
High Temp
OperatorRe-startsCooling
OperatorShuts Down
Result
Shutdown = 0.2450 + 0.001856 + 0.00001688 + 0.0006187 = 0.2475 occurrences/yr.
Runaway = 0.0002475 + 0.000001875 + 0.000000625 = 0.0002500 occurrences/yr.
Figure 11-11 Event tree for the reactor of Figure 11-8. This includes a high temperature shutdown system.
Initiating Event:
Loss of Cooling
1 Occurrence/yr.
A
1
A0.7425
0.99
0.01
0.2475
0.001875
0.000625
0.00750
0.0025
Continue Operation
Shut Down
Shut Down
Runaway
OperatorShuts Down
Reactor
AD0.2450
ADE0.002228
ADEF0.0002475
AB0.005625
ABD0.001856
ABDE0.00001688
ABDEF0.000001875ABC0.001875
ABCD0.0006187
ABCDE0.00000563
ABCDEF0.000000625
0.002475
0.00001875
0.00000675
Continue Operation
Shut Down
Shut Down
Runaway
Continue Operation
Shut Down
Shut Down
Runaway
ADVANTAGES
• Structured, rigorous, and methodical approach.
• Can be effectively performed on varying levels of design detail.
• Permits probability assessment.
DISADVANTAGES
• An ETA can only have one initiating event, therefore multiple ETAs will be required to evaluate the consequence of multiple initiating events.
• Partial successes/failures are not distinguishable.
• Requires an analyst with some training and practical experience.
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