Benefits of Bayesian Network Models

<p>Foreword by J.–F. Aubry ix</p>
<p>Foreword by L. Portinale&nbsp; xiii</p>
<p>Acknowledgments&nbsp; xv</p>
<p>Introduction xvii</p>
<p>Part 1. Bayesian Networks 1</p>
<p>Chapter 1. Bayesian Networks: a Modeling Formalism for System Dependability&nbsp; 3</p>
<p>1.1. Probabilistic graphical models: BN&nbsp; 5</p>
<p>1.1.1. BN: a formalism to model dependability&nbsp; 5</p>
<p>1.1.2. Inference mechanism&nbsp; 7</p>
<p>1.2. Reliability and joint probability distributions 8</p>
<p>1.2.1. Multi–state system example&nbsp; 8</p>
<p>1.2.2. Joint distribution&nbsp; 9</p>
<p>1.2.3. Reliability computing&nbsp; 9</p>
<p>1.2.4. Factorization 10</p>
<p>1.3. Discussion and conclusion 14</p>
<p>Chapter 2. Bayesian Network: Modeling Formalism of the Stucture Function of Boolean Systems 17</p>
<p>2.1. Introduction 17</p>
<p>2.2. BN models in the Boolean case&nbsp; 19</p>
<p>2.2.1. BN model from cut–sets&nbsp; 20</p>
<p>2.2.2. BN model from tie–sets 23</p>
<p>2.2.3. BN model from a top–down approach 25</p>
<p>2.2.4. BN model of a bowtie 26</p>
<p>2.3. Standard Boolean gates CPT&nbsp; 29</p>
<p>2.4. Non–deterministic CPT 31</p>
<p>2.5. Industrial applications&nbsp; 38</p>
<p>2.6. Conclusion&nbsp; 41</p>
<p>Chapter 3. Bayesian Network: Modeling Formalism of the Structure Function of Multi–State Systems&nbsp; 43</p>
<p>3.1. Introduction 43</p>
<p>3.2. BN models in the multi–state case 43</p>
<p>3.2.1. BN model of multi–state systems from tie–sets 44</p>
<p>3.2.2. BN model of multi–state systems from cut–sets&nbsp; 49</p>
<p>3.2.3. BN model of multi–state systems from functional and dysfunctional analysis 52</p>
<p>3.3. Non–deterministic CPT 58</p>
<p>3.4. Industrial applications&nbsp; 59</p>
<p>3.5. Conclusion&nbsp; 62</p>
<p>Part 2. Dynamic Bayesian Networks 65</p>
<p>Chapter 4. Dynamic Bayesian Networks: Integrating Environmental and Operating Constraints in Reliability Computation 67</p>
<p>4.1. Introduction 67</p>
<p>4.2. Component modeled by a DBN&nbsp; 69</p>
<p>4.2.1. DBN model of a MC&nbsp; 70</p>
<p>4.2.2. DBN model of non–homogeneous MC&nbsp; 71</p>
<p>4.2.3. Stochastic process with exogenous constraint&nbsp; 72</p>
<p>4.3. Model of a dynamic multi–state system&nbsp; 75</p>
<p>4.4. Discussion on dependent processes&nbsp; 79</p>
<p>4.5. Conclusion&nbsp; 81</p>
<p>Chapter 5. Dynamic Bayesian Networks: Integrating Reliability Computation in the Control System&nbsp; 83</p>
<p>5.1. Introduction 83</p>
<p>5.2. Integrating reliability information into the control 84</p>
<p>5.3. Control integrating reliability modeled by DBN&nbsp; 85</p>
<p>5.3.1. Modeling and controlling an over–actuated system&nbsp; 86</p>
<p>5.3.2. Integrating reliability&nbsp; 88</p>
<p>5.4. Application to a drinking water network 90</p>
<p>5.4.1. DBN modeling 91</p>
<p>5.4.2. Results and discussion 92</p>
<p>5.5. Conclusion 95</p>
<p>5.6. Acknowledgments&nbsp; 96</p>
<p>Conclusion 97</p>
<p>Bibliography&nbsp; 101</p>
<p>Index 113</p>