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# Fault Tree Analysis

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### Fault Tree Analysis

1. 1. Presented by K.CHELLAMUTHU FAULT TREE ANALYSIS UNIT - 3
2. 2. DEFINITION <ul><li>Fault Tree Analysis (FTA) is one of the most important logic and probabilistic techniques used in Probabilistic Risk Assessment (PRA) and system reliability assessment. </li></ul><ul><li>Fault Tree Analysis (FTA) attempts to model and analyze failure processes of engineering systems. FTA can be simply described as an analytical technique </li></ul>
3. 3. METHODOLOGY <ul><li>In the technique known as &quot;fault tree analysis&quot;, an undesired effect is taken as the root ('top event') of a tree of logic. </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul><ul><li>The shortest credible way through the tree from fault to initiating event is called a Minimal Cut Set. </li></ul>
4. 4. STEPS IN CARRYING OUT A FAULT TREE ANALYSIS <ul><li>Identify the objective for the FTA. </li></ul><ul><li>2. Define the top event of the FT. </li></ul><ul><li>Define the scope of the FTA. </li></ul><ul><li>4. Define the resolution of the FTA. </li></ul><ul><li>Define ground rules for the FTA. </li></ul><ul><li>* The first five steps involve the problem formulation for an FTA . </li></ul><ul><li>6. Construct the FT. </li></ul><ul><li>7. Evaluate the FT. </li></ul><ul><li>Interpret and present the results. </li></ul><ul><li>The remaining steps involve the actual construction of the FT, the evaluation of the FT, and the interpretation of the FT results. </li></ul>
5. 5. 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
6. 6. FAULT TREE CONSTRUCTION` <ul><li>Consider the following block diagram. Let I/P and O/P be the input </li></ul><ul><li>And output terminals. There are two sub-systems A and B that are connected in series. </li></ul>INPUT OUTPUT X 1 X 3 X 2 X 4 SUB - SYSTEM (A) SUB - SYSTEM (B) For this the fault tree analysis diagram shown in next slide
7. 7. F (S) F (A) F (B) F( X 1) F( X 3) F( X 2) F( X 4) AND OR AND
8. 8. CONTINUE….. <ul><li>Here F(x1) , F(x2) , F(x3), F(x4) Are Events Fail… </li></ul><ul><li>F (A) = SUB – SYSTEM (A) FAILS </li></ul><ul><li>F(B) = SUB – SYSTEM (B) FAILS </li></ul><ul><li>THEN F(A) = F(X1) AND F(X2) </li></ul><ul><li>AND F(B) = F(X3) AND F(X4) </li></ul><ul><li>FINALLY THE FAILURE OF THE SYSTEM </li></ul><ul><li>F(S) = F(A) OR F(B) </li></ul>
9. 9. CALCULATION OF RELIABILITY FROM FAULT TREE <ul><li>CONSIDER THE EARLIER BLOCK DIAGRAM </li></ul><ul><li> The probability of failure of sub – system (A) is indicated as shown in below, </li></ul><ul><li> P(A) = P (X 1 and X 2) </li></ul><ul><li> P(A) = P( X1) * P( X 2) </li></ul><ul><li>Similarly for sub – system (B) </li></ul><ul><li> P(B) = P( X 3 and X 4) </li></ul><ul><li> P(B) = P( X 3) * P( X 4) </li></ul><ul><li>FAILURE OCCURS WHEN SUB – SYSTEM (A) or (B) FAIL.., </li></ul><ul><li>F (S) = P(A) or P(B) THEN F(S) = P(A) + P(B) – ( P(A) * P(B) ) </li></ul><ul><li>IF THE RELIABILITY OF THE ELEMENTS ARE GIVEN BY R1,R2,R3,R4 </li></ul><ul><li>THEN </li></ul><ul><li>P( X i ) = 1 – Ri </li></ul><ul><li> RELIABILITY OF SYSTEM R(S) = 1 - F(S) </li></ul><ul><li> </li></ul>
10. 10. <ul><li>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. </li></ul>mains transformer generator Operation theatre
11. 11. BLOCK DIAGRAM X 1 X 2 X 3 INPUT OUTPUT
12. 12. Fault tree for problem F (S) AND OR A B C Main fails Transformer fails Generator fails
13. 13. SOLUTION <ul><li>FAILURE OF THE SYSTEM </li></ul><ul><li>F (S) = ( P ( X1 ) or P(X 2) ) and P( X 3 ) </li></ul><ul><li>P ( X 1) = 0.01 </li></ul><ul><li>P ( X 2) = 1 – 0.996 = 0.004 </li></ul><ul><li>P ( X 3) = 1 – 0.99 = 0.001 </li></ul><ul><li>F (S) = ( P (X 1) + P (X 2 ) – ( P (X1 ) * P(X2) ) ) * ( P (X 3 ) ) </li></ul><ul><li>= ( 0.01 + 0.004 – ( 0.01 * 0.004) ) * (0.001) </li></ul><ul><li>F(S) = 0.0001396 </li></ul><ul><li>FOR RELIABILITY </li></ul><ul><li>R(S) = 1- F(S) </li></ul><ul><li> = 1- 0.0001396 </li></ul><ul><li>R(S) = 0.99986 </li></ul>
14. 14. USES <ul><li>Use of FTA to understand of the logic leading to the top event. </li></ul><ul><li>Use of FTA to prioritize the contributors leading to the top event. </li></ul><ul><li>Use of FTA as a proactive tool to prevent the top event. </li></ul><ul><li>Use of FTA to monitor the performance of the system. </li></ul><ul><li>Use of FTA to minimize and optimize resources. </li></ul><ul><li>Use of FTA to assist in designing a system. </li></ul><ul><li>Use of FTA as a diagnostic tool to identify and correct causes of the top event. </li></ul>
15. 15. THANK YOU