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 Tree Analysis (FTA) attempts to model and analyze failure processes of engineering systems. FTA can be simply described as an analytical technique

METHODOLOGY

In the technique known as "fault tree analysis", an undesired effect is taken as the root ('top event') of a tree of logic.

There should be only one Top Event and all concerns must tree down from it. Then, each situation that could cause that effect is added to the tree as a series of logic expressions.

The Tree is usually written out using conventional logic gate symbols. The route through a tree between an event and an initiator in the tree is called as Cut Set.

The shortest credible way through the tree from fault to initiating event is called a Minimal Cut Set.

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

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 TREECONSIDER 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.