1. Process of Diagnosing a Dynamic System Lab Seminar June 19th, 2007 Seung Ki Shin

2. Korea Advanced Institute of Science and Technology Contents  Introduction  Process of diagnosing a dynamic system  Sensitivity analysis  Diagnostics importance factor  Diagnostic decision tree  Example (Active Heat Rejection System)  Conclusion 1/13

3. Korea Advanced Institute of Science and Technology Introduction  The ability to perform system diagnostics on a failed system has a huge impact on system’s life-time quality and the overall cost of repair.  It will be demonstrated how a diagnostics procedure can be performed on a dynamic system.  To be able to diagnose a dynamic system, we have to answer some questions.  Which components have failed when the system has failed?  Which components have to be repaired to bring the system up?  How does the logical structure of the system effect the diagnostic process?  How do we select which components to check first and which last? 2/13

4. Korea Advanced Institute of Science and Technology Process of diagnosing a dynamic system ① Generating the Markov chain from the dynamic fault tree ② Sensitivity analysis ③ Measuring the diagnostics importance factor (DIF) for compoonents ④ Obtaining minimal cut set/sequence ⑤ Drawing diagnostic decision tree 3/13

5. Korea Advanced Institute of Science and Technology Process of diagnosing a dynamic system  Sensitivity analysis  Sensitivity values are also known as Marginal Importance Factors (MIF) or Birnbaum importance factor (I b ).  The sensitivity is a partial derivative of the probability of system failure with respect to component failure.   For static fault trees, Rauzy has developed a method to obtain this measure based on Binary Decision Diagrams.  For dynamic fault trees, Ou and Dugan have developed an approximate method to calculate the sensitivity based on Markov chain.   q i : the component’s in-system unreliability  Q i : the sum of the probabilities being in failed states with basic event i failed.  Q ī : the sum of the probabilities being in failed states with basic event i operational. 4/13

6. Korea Advanced Institute of Science and Technology Process of diagnosing a dynamic system  Diagnostics importance factor  Probability that a component event has occurred given the top event has occurred.   Rauzy showed how to obtain the DIF measures if the MIF measures are known.  5/13

7. Korea Advanced Institute of Science and Technology Process of diagnosing a dynamic system  Diagnostic decision tree  General objective of the DDT is to provide a guide for system diagnosis and repair with focusing on trying to bring the failing cut sets/sequences up with testing every component.  The order by which cutsets are checked depends on the DIF ordering.  Components with cutsets of higher importance are checked first.  When a cutset is repaired, the status of the system is checked and if it is still inoperative we move on to the next cutset until we find the problem. 6/13

8. Korea Advanced Institute of Science and Technology Example (Active Heat Rejection System)  Description  This system consists of two sets of components (A1&A2) and (B1&B2).  A2 and B2 are backup. (Cold spare)  At least one of (A1&A2) and at least one of (B1&B2) are required for system operation.  Loss of power means loss of supplied components. 7/13

9. Korea Advanced Institute of Science and Technology Example (Active Heat Rejection System) ① Dynamic fault tree & Markov chain  Dynamic fault tree  Markov chain 8/13 Component Failure rate P of F A10.0010.3294 A20.0050.1525 B10.0020.3907 B20.00350.1559 P10.0030.2591 P20.0030.2565

10. Korea Advanced Institute of Science and Technology Example (Active Heat Rejection System) ② Sensitivity analysis  (i.e.) i = A2 ComponentSensitivity A1 0.199645 A2 0.20458 B1 0.160472 B2 0.241436 P1 0.477353 P2 0.353707  Sensitivity table 9/13

11. Korea Advanced Institute of Science and Technology Example (Active Heat Rejection System) ③ Diagnostics importance factor  ComponentDIF A1 0.508199 A2 0.259699 B1 0.545579 B2 0.284713 P1 0.630623 P2 0.529983  DIF table ④ Minimal cut sets/sequences MCS {P1, P2} {P1, B1} {P1, A2} {B2, P2} {B1, B2} {A1, P2} {A1, A2} 10/13

12. Korea Advanced Institute of Science and Technology Example (Active Heat Rejection System) ⑤ Diagnostic decision tree 1. Test P1. (highest DIF value) 2. Split the cutsets into those with P1 and those without: a) If P1 failed test, take the set of cutsets that include P1. - Look for the component that has next highest DIF after P1. (B1) - Recursively repeat steps 1~2. b) If P1 has not failed test, take another cutset. - Look for the component that has next highest DIF. (B1) - Recursively repeat steps 1~2. 11/13

13. Korea Advanced Institute of Science and Technology Conclusion  Diagnostic decision tree allows the maintenance crew to make more efficient decisions when trying to repair a system.  It provides us with a map that allows us to recognize the failing components, and inform us which ones need repair.  It allows ranking components by their relevance from a diagnostics perspective.  The experience or expertise of the crew becomes less relevant. 12/13

14. Korea Advanced Institute of Science and Technology References  T. Assaf and J. B. Dugan, “Diagnostic Expert Systems from Dynamic Fault Trees”, Proceedings of the Annual Reliability and Maintainability Symposium, 2004.  T. Assaf and J. B. Dugan, “Automatic Generation of Diagnostic Expert Systems from Fault Trees”, Proceedings of the Annual Reliability and Maintainability Symposium, 2003.  Y. Dutuit and A. Rauzy, “Efficient algorithms to assess component and gate importance in fault tree analysis”, Reliability Engineering and System Safety, 2001. 13/13