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Fault Tree Analysis

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  • 1. Presented by K.CHELLAMUTHU FAULT TREE ANALYSIS UNIT - 3
  • 2. 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
  • 3. 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.
  • 4. STEPS IN CARRYING OUT A FAULT TREE ANALYSIS
    • Identify the objective for the FTA.
    • 2. Define the top event of the FT.
    • Define the scope of the FTA.
    • 4. Define the resolution of the FTA.
    • 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.
    • 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.
  • 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. FAULT TREE CONSTRUCTION`
    • Consider the following block diagram. Let I/P and O/P be the input
    • And output terminals. There are two sub-systems A and B that are connected in series.
    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. F (S) F (A) F (B) F( X 1) F( X 3) F( X 2) F( X 4) AND OR AND
  • 8. 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)
  • 9. CALCULATION OF RELIABILITY FROM 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
    • THEN
    • P( X i ) = 1 – Ri
    • RELIABILITY OF SYSTEM R(S) = 1 - F(S)
  • 10.
    • 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
  • 11. BLOCK DIAGRAM X 1 X 2 X 3 INPUT OUTPUT
  • 12. Fault tree for problem F (S) AND OR A B C Main fails Transformer fails Generator fails
  • 13. SOLUTION
    • FAILURE 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 RELIABILITY
    • R(S) = 1- F(S)
    • = 1- 0.0001396
    • R(S) = 0.99986
  • 14. 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.
  • 15. THANK YOU