Systems Dependability Assessment

Pr. Jean-François AUBRY Professor Emeritus, University of Lorraine, France. Dr. Nicolae BRINZEI, Associate Professor, University of Lorraine, France.

• PREFACE ixINTRODUCTION xiiiPART 1. PREDICTED RELIABILITY OF STATIC SYSTEMS; A GRAPH-THEORY BASED APPROACH 1CHAPTER 1. STATIC AND TIME INVARIANT SYSTEMS WITH BOOLEAN REPRESENTATION 31.1. Notations 31.2. Order relation on U 41.3. Structure of a system 61.3.1. State diagram of a system 61.3.2. Monotony of an SF, coherence of a system 71.4. Cut-set and tie-set of a system 91.4.1. Tie-set 91.4.2. Cut-set 10CHAPTER 2. RELIABILITY OF A COHERENT SYSTEM 132.1. Demonstrating example 152.2. The reliability block diagram (RBD) 182.3. The fault tree (FT) 212.4. The event tree 262.5. The structure function as a minimal union of disjoint monomials 282.5.1. Ordered graph of a monotone structure function 292.5.2. Maxima and minima of the ordered graph 312.5.3. Ordered subgraphs of the structure function 322.5.4. Introductory example 332.5.5. Construction of the minimal Boolean form 372.5.6. Complexity 432.5.7. Comparison with the BDD approach 452.6. Obtaining the reliability equation from the Boolean equation 492.6.1. The traditional approach 492.6.2. Comparison with the structure function by Kaufmann 502.7. Obtain directly the reliability from the ordered graph 522.7.1. Ordered weighted graph 532.7.2. Algorithm 562.7.3. Performances of the algorithm 59CHAPTER 3. WHAT ABOUT NON-COHERENT SYSTEMS? 613.1. Example of a non-coherent supposed system 613.2. How to characterize the non-coherence of a system? 633.3. Extension of the ordered graph method 663.3.1. Decomposition algorithm 673.4. Generalization of the weighted graph algorithm 68CONCLUSION TO PART 1 73PART 2. PREDICTED DEPENDABILITY OF SYSTEMS IN A DYNAMIC CONTEXT 75INTRODUCTION TO PART 2 77CHAPTER 4. FINITE STATE AUTOMATON 834.1. The context of discrete event system 834.2. The basic model 84CHAPTER 5. STOCHASTIC FSA 895.1. Basic definition 895.2. Particular case: Markov and semi-Markov processes 905.3. Interest of the FSA model 915.4. Example of stochastic FSA 925.5. Probability of a sequence 935.6. Simulation with Scilab 945.7. State/event duality 955.8. Construction of a stochastic SFA 96CHAPTER 6. GENERALIZED STOCHASTIC FSA 101CHAPTER 7. STOCHASTIC HYBRID AUTOMATON 1057.1. Motivation 1057.2. Formal definition of the model 1057.3. Implementation 1077.4. Example 1097.5. Other examples 1167.5.1. Control temperature of an oven 1167.5.2. Steam generator of a nuclear power plant 1187.6. Conclusion 120CHAPTER 8. OTHER MODELS/TOOLS FOR DYNAMIC DEPENDABILITY VERSUS SHA 1218.1. The dynamic fault trees 1218.1.1. Principle 1218.1.2. Equivalence with the FSA approach 1248.1.3. Covered criteria 1268.2. The Boolean logic-driven Markov processes 1268.2.1. Principle 1268.2.2. Equivalence with the FSA approach 1278.2.3. Covered criteria 1278.3. The dynamic event trees (DETs) 1288.3.1. Principle 1288.3.2. Equivalence with the FSA approach 1298.3.3. Covered criteria 1308.4. The piecewise deterministic Markov processes 1318.4.1. Principle 1318.4.2. Equivalence with the FSA approach 1318.4.3. Covered criteria 1328.5. Other approaches 132CONCLUSION AND PERSPECTIVES 135APPENDIX 137BIBLIOGRAPHY 173INDEX 181