Binary decision diagrams and extensions for system reliability analysis - Xing, Liudong (John Wiley and Sons, Inc., 2015)
Machine generated contents note: Preface xiii Nomenclature xix 1 Introduction 1 1.1 Historical Developments 1 1.2 Reliability and Safety Applications 4 2 Basic Reliability Theory and Models 7 2.1 Probabiltiy Concepts 7 2.2 Reliability Measures 14 2.3 Fault Tree Analysis 17 3 Fundamentals of Binary Decision Diagrams 33 3.1 Preliminaries 34 3.2 Basic Concepts 34 3.3 BDD Construction 35 3.4 BDD Evaluation 42 3.5 BDD-Based Software Package 44 4 Application of BDD to Binary-State Systems 45 4.1 Network Reliability Analysis 45 4.2 Event Tree Analysis 47 4.3 Failure Frequency Analysis 50 4.4 Importance Measures and Analysis 54 4.5 Modularization Methods 60 4.6 Non-Coherent Systems 60 4.7 Disjoint Failures 65 4.8 Dependent Failures 68 5 Phased-Mission Systems 73 5.1 System Description 74 5.2 Rules of Phase Algebra 75 5.3 BDD-Based Method for PMS Analysis 76 5.4 Mission Performance Analysis 81 6 Multi-State Systems 85 6.1 Assumptions 86 6.2 An Illustrative Example 86 6.3 MSS Representation 87 6.4 Multi-State BDD (MBDD) 90 6.5 Logarithmically-Encoded BDD (LBDD) 94 6.6 Multi-State Multi-Valued Decision Diagrams (MMDD) 98 6.7 Performance Evaluation and Benchmarks 102 6.8 Summary 117 7 Fault Tolerant Systems and Coverage Models 119 7.1 Basic Types 120 7.2 Imperfect Coverage Model 122 7.3 Applications to Binary-State Systems 123 7.4 Applications to Multi-State Systems 129 7.5 Applications to Phased-Mission Systems 133 7.6 Summary 139 8 Shared Decision Diagrams 143 8.1 Multi-Rooted Decision Diagrams 144 8.2 Multi-Terminal Decision Diagrams 148 8.3 Performance Study on Multi-State Systems 151 8.4 Application to Phased-Mission Systems 163 8.5 Application to Multi-State k-out-of-n Systems 168 8.6 Importance Measures 176 8.7 Failure Frequency Based Measures 180 8.8 Summary 183 Conclusions 185 References 187 Index 205 .