FAULT & EVENT TREE ANALYSIS

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



at temperature T1



reactor


INITIATING EVENT:


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



at temperature T1



reactor


INITIATING EVENT:


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



at temperature T1



reactor


INITIATING EVENT:


COMPLETED EVENT TREE

Success

Failure

Completed !

Step 4: Describe the Accident Sequence

SAFETYFUNCTION



at temperature T1



reactor


INITIATING EVENT:


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.

FAULT & EVENT TREE ANALYSIS

Education

Transcript of FAULT & EVENT TREE ANALYSIS