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Systems Dependability Assessment


Systems Dependability Assessment

Modeling with Graphs and Finite State Automata
1. Aufl.

von: Jean-Francois Aubry, Nicolae Brinzei

139,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 02.02.2015
ISBN/EAN: 9781119053927
Sprache: englisch
Anzahl Seiten: 198

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Beschreibungen

<p>Presents recent developments of probabilistic assessment of systems dependability based on stochastic models, including graph theory, finite state automaton and language theory, for both dynamic and hybrid contexts.</p>
<p>PREFACE ix</p> <p>INTRODUCTION xiii</p> <p><b>PART 1. PREDICTED RELIABILITY OF STATIC SYSTEMS; A GRAPH-THEORY BASED APPROACH 1</b></p> <p><b>CHAPTER 1. STATIC AND TIME INVARIANT SYSTEMS WITH BOOLEAN REPRESENTATION 3</b></p> <p>1.1. Notations 3</p> <p>1.2. Order relation on U 4</p> <p>1.3. Structure of a system 6</p> <p>1.3.1. State diagram of a system 6</p> <p>1.3.2. Monotony of an SF, coherence of a system 7</p> <p>1.4. Cut-set and tie-set of a system 9</p> <p>1.4.1. Tie-set 9</p> <p>1.4.2. Cut-set 10</p> <p><b>CHAPTER 2. RELIABILITY OF A COHERENT SYSTEM 13</b></p> <p>2.1. Demonstrating example 15</p> <p>2.2. The reliability block diagram (RBD) 18</p> <p>2.3. The fault tree (FT) 21</p> <p>2.4. The event tree 26</p> <p>2.5. The structure function as a minimal union of disjoint monomials 28</p> <p>2.5.1. Ordered graph of a monotone structure function 29</p> <p>2.5.2. Maxima and minima of the ordered graph 31</p> <p>2.5.3. Ordered subgraphs of the structure function 32</p> <p>2.5.4. Introductory example 33</p> <p>2.5.5. Construction of the minimal Boolean form 37</p> <p>2.5.6. Complexity 43</p> <p>2.5.7. Comparison with the BDD approach 45</p> <p>2.6. Obtaining the reliability equation from the Boolean equation 49<br /><br />2.6.1. The traditional approach 49</p> <p>2.6.2. Comparison with the structure function by Kaufmann 50</p> <p>2.7. Obtain directly the reliability from the ordered graph 52</p> <p>2.7.1. Ordered weighted graph 53</p> <p>2.7.2. Algorithm 56</p> <p>2.7.3. Performances of the algorithm 59</p> <p><b>CHAPTER 3. WHAT ABOUT NON-COHERENT SYSTEMS? 61</b></p> <p>3.1. Example of a non-coherent supposed system 61</p> <p>3.2. How to characterize the non-coherence of a system? 63</p> <p>3.3. Extension of the ordered graph method 66</p> <p>3.3.1. Decomposition algorithm 67</p> <p>3.4. Generalization of the weighted graph algorithm 68</p> <p>CONCLUSION TO PART 1 73</p> <p><b>PART 2. PREDICTED DEPENDABILITY OF SYSTEMS IN A DYNAMIC CONTEXT 75</b></p> <p><b>INTRODUCTION TO PART 2 77</b></p> <p><b>CHAPTER 4. FINITE STATE AUTOMATON 83</b></p> <p>4.1. The context of discrete event system 83</p> <p>4.2. The basic model 84</p> <p><b>CHAPTER 5. STOCHASTIC FSA 89</b></p> <p>5.1. Basic definition 89</p> <p>5.2. Particular case: Markov and semi-Markov processes 90</p> <p>5.3. Interest of the FSA model 91</p> <p>5.4. Example of stochastic FSA 92</p> <p>5.5. Probability of a sequence 93</p> <p>5.6. Simulation with Scilab 94</p> <p>5.7. State/event duality 95</p> <p>5.8. Construction of a stochastic SFA 96</p> <p><b>CHAPTER 6. GENERALIZED STOCHASTIC FSA 101</b></p> <p><b>CHAPTER 7. STOCHASTIC HYBRID AUTOMATON 105</b></p> <p>7.1. Motivation 105</p> <p>7.2. Formal definition of the model 105</p> <p>7.3. Implementation 107</p> <p>7.4. Example 109</p> <p>7.5. Other examples 116</p> <p>7.5.1. Control temperature of an oven 116</p> <p>7.5.2. Steam generator of a nuclear power plant 118</p> <p>7.6. Conclusion 120</p> <p><b>CHAPTER 8. OTHER MODELS/TOOLS FOR DYNAMIC DEPENDABILITY VERSUS SHA 121</b></p> <p>8.1. The dynamic fault trees 121</p> <p>8.1.1. Principle 121</p> <p>8.1.2. Equivalence with the FSA approach 124</p> <p>8.1.3. Covered criteria 126</p> <p>8.2. The Boolean logic-driven Markov processes 126</p> <p>8.2.1. Principle 126</p> <p>8.2.2. Equivalence with the FSA approach 127</p> <p>8.2.3. Covered criteria 127</p> <p>8.3. The dynamic event trees (DETs) 128</p> <p>8.3.1. Principle 128</p> <p>8.3.2. Equivalence with the FSA approach 129</p> <p>8.3.3. Covered criteria 130</p> <p>8.4. The piecewise deterministic Markov processes 131</p> <p>8.4.1. Principle 131</p> <p>8.4.2. Equivalence with the FSA approach 131</p> <p>8.4.3. Covered criteria 132</p> <p>8.5. Other approaches 132</p> <p>CONCLUSION AND PERSPECTIVES 135</p> <p>APPENDIX 137</p> <p>BIBLIOGRAPHY 173</p> <p>INDEX 181</p>
<p><strong>Pr. Jean-François AUBRY</strong> Professor Emeritus, University of Lorraine, France. <p><strong>Dr. Nicolae BRINZEI<strong>, Associate Professor, University of Lorraine, France.

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