Benefits of Bayesian Network Models

Philippe Weber is Professor at the Engineer School of Sciences and Technologies at the University of Lorraine and at the Research Centre for Automatic Control in Nancy, France. His research concerns dependability and is mainly focused on probabilistic graphical models. Christophe Simon is Associate Professor at the Research Centre for Automatic Control in Nancy, France. His research concerns dependability and is mainly focused on modeling engineering and uncertainties.

• Foreword by J.-f Aubry ixForeword by l Portinale xiiiAcknowledgments xvIntroduction xviiPart 1 Bayesian Networks 1Chapter 1 Bayesian Networks: a Modeling Formalism for System Dependability 31.1 Probabilistic graphical models: BN 51.1.1 BN: a formalism to model dependability 51.1.2 Inference mechanism 71.2 Reliability and joint probability distributions 81.2.1 Multi-state system example 81.2.2 Joint distribution 91.2.3 Reliability computing 91.2.4 Factorization 101.3 Discussion and conclusion 14Chapter 2 Bayesian Network: Modeling Formalism of the Stucture Function of Boolean Systems 172.1 Introduction 172.2 BN models in the Boolean case 192.2.1 BN model from cut-sets 202.2.2 BN model from tie-sets 232.2.3 BN model from a top-down approach 252.2.4 BN model of a bowtie 262.3 Standard Boolean gates CPT 292.4 Non-deterministic CPT 312.5 Industrial applications 382.6 Conclusion 41Chapter 3 Bayesian Network: Modeling Formalism of the Structure Function of Multi-State Systems 433.1 Introduction 433.2 BN models in the multi-state case 433.2.1 BN model of multi-state systems from tie-sets 443.2.2 BN model of multi-state systems from cut-sets 493.2.3 BN model of multi-state systems from functional and dysfunctional analysis 523.3 Non-deterministic CPT 583.4 Industrial applications 593.5 Conclusion 62Part 2 Dynamic Bayesian Networks 65Chapter 4 Dynamic Bayesian Networks: Integrating Environmental and Operating Constraints in Reliability Computation 674.1 Introduction 674.2 Component modeled by a DBN 694.2.1 DBN model of a MC 704.2.2 DBN model of non-homogeneous MC 714.2.3 Stochastic process with exogenous constraint 724.3 Model of a dynamic multi-state system 754.4 Discussion on dependent processes 794.5 Conclusion 81Chapter 5 Dynamic Bayesian Networks: Integrating Reliability Computation in the Control System 835.1 Introduction 835.2 Integrating reliability information into the control 845.3 Control integrating reliability modeled by DBN 855.3.1 Modeling and controlling an over-actuated system 865.3.2 Integrating reliability 885.4 Application to a drinking water network 905.4.1 DBN modeling 915.4.2 Results and discussion 925.5 Conclusion 955.6 Acknowledgments 96Conclusion 97Bibliography 101Index 113