Foreword ix
Preface xi
Nomenclature xv
1 Introduction 1
References 4
2 Fundamental Reliability Theory 7
2.1 Basic Probability Concepts 7
2.1.1 Axioms of Probability 7
2.1.2 Conditional Probability 7
2.1.3 Total Probability Law 8
2.1.4 Bayes' Theorem 9
2.1.5 Random Variables 9
2.2 Reliability Measures 10
2.2.1 Time to Failure 11
2.2.2 Failure Function 11
2.2.3 Reliability Function 11
2.2.4 Failure Rate 11
2.2.5 Mean Time to Failure 11
2.2.6 Mean Residual Life 12
2.3 Fault Tree Modeling 12
2.3.1 Static Fault Tree 13
2.3.2 Dynamic Fault Tree 13
2.3.3 Phased-Mission Fault Tree 14
2.3.4 Multi-State Fault Tree 15
2.4 Binary Decision Diagram 16
2.4.1 Basic Concept 17
2.4.2 ROBDD Generation 17
2.4.3 ROBDD Evaluation 18
2.4.4 Illustrative Example 19
2.5 Markov Process 20
2.6 Reliability Software 22
References 22
3 Imperfect Fault Coverage 27
3.1 Different Types of IPC 27
3.2 ELC Modeling 28
3.3 Binary-State System 29
3.3.1 BDD Expansion Method 29
3.3.2 Simple and Efficient Algorithm 32
3.4 Multi-State System 34
3.4.1 MMDD-Based Method for MSS Analysis 35
3.4.2 Illustrative Example 36
3.5 Phased-Mission System 37
3.5.1 Mini-Component Concept 37
3.5.2 PMS SEA 38
3.5.3 PMS BDD Method 40
3.5.4 Summary of PMS SEA 42
3.5.5 Illustrative Example 42
3.6 Summary 43
References 45
4 Modular Imperfect Coverage 49
4.1 Modular Imperfect Coverage Model 49
4.2 Non repairable Hierarchical System 51
4.3 Repairable Hierarchical System 55
4.4 Summary 58
References 58
5 Functional Dependence 61
5.1 Logic OR Replacement Method 61
5.2 Combinatorial Algorithm 63
5.2.1 Task 1: Addressing UFs of Independent Trigger Components 63
5.2.2 Task 2: Generating Reduced Problems Without FDEP 63
5.2.3 Task 3: Solving Reduced Reliability Problems 64
5.2.3.1 Expansion Process 64
5.2.3.2 Reduced FT Generation Procedure 65
5.2.3.3 Dual Trigger-Basic Event Handling 65
5.2.3.4 Evaluation of P(system fails|ITEi) 65
5.2.4 Task 4: Integrating to Obtain Final System Unreliability 66
5.2.5 Algorithm Summary 66
5.2.6 Algorithm Complexity 66
5.3 Case Study 1: Combined Trigger Event 67
5.4 Case Study 2: Shared Dependent Event 70
5.5 Case Study 3: Cascading FDEP 73
5.5.1 Evaluation of P(system fails|ITE1) 74
5.5.2 Evaluation of P(system fails|ITE2) 75
5.5.3 Evaluation of URsystem 76
5.6 Case Study 4: Dual Event and Cascading FDEP 76
5.6.1 Evaluation of P(system fails|ITE1) 78
5.6.2 Evaluation of URsystem 79
5.7 Summary 79
References 80
6 Deterministic Common-Cause Failure 83
6.1 Explicit Method 84
6.1.1 Two-Step Method 84
6.1.2 Illustrative Example 84
6.2 Efficient Decomposition and Aggregation Approach 85
6.2.1 Three-Step Method 86
6.2.2 Illustrative Example 87
6.3 Decision Diagram-Based Aggregation Method 89
6.3.1 Three-Step Method 89
6.3.2 Illustrative Example 91
6.4 Universal Generating Function-Based Method 94
6.4.1 System Model 94
6.4.2 u-Function Method for Series-Parallel Systems 95
6.4.3 u-Function Method for CCFs 97
6.4.4 Illustrative Example 99
6.5 Summary 104
References 104
7 Probabilistic Common-Cause Failure 107
7.1 Single-Phase System 107
7.1.1 Explicit Method 108
7.1.2 Implicit Method 110
7.1.3 Comparisons and Discussions 115
7.2 Multi-Phase System 115
7.2.1 Explicit Method 115
7.2.2 Implicit Method 119
7.2.3 Comparisons and Discussions 123
7.3 Impact of PCCF 124
7.4 Summary 125
References 125
8 Deterministic Competing Failure 127
8.1 Overview 127
8.2 PFGE Method 128
8.2.1 s-Independent LF and PFGE 128
8.2.2 s-Dependent LF and PFGE 128
8.2.3 Disjoint LF and PFGE 129
8.3 Single-Phase System with Single FDEP Group 129
8.3.1 Combinatorial Method 129
8.3.2 Case Study 131
8.4 Single-Phase System with Multiple FDEP Groups 135
8.4.1 Combinatorial Method 135
8.4.2 Case Study 137
8.5 Single-Phase System with PFs Having Global and Selective Effects 141
8.5.1 Combinatorial Method 141
8.5.2 Case Study 144
8.6 Multi-Phase System with Single FDEP Group 150
8.6.1 Combinatorial Method 150
8.6.2 Case Study 153
8.7 Multi-Phase System with Multiple FDEP Groups 158
8.7.1 CTMC-Based Method 158
8.7.2 Case Study 159
8.8 Summary 166
References 167
9 Probabilistic Competing Failure 169
9.1 Overview 169
9.2 System with Single Type of Component Local Failures 170
9.2.1 Combinatorial Method 170
9.2.2 Case Study 172
9.3 System with Multiple Types of Component Local Failures 181
9.3.1 Combinatorial Method 181
9.3.2 Case Study 182
9.4 System with Random Failure Propagation Time 190
9.4.1 Combinatorial Method 190
9.4.2 Case Study: WSN System 192
9.5 Summary 198
References 199
10 Dynamic Standby Sparing 201
10.1 Types of Standby Systems 201
10.2 CTMC-Based Method 202
10.2.1 Cold Standby System 203
10.2.2 Warm Standby System 204
10.3 Decision Diagram?Based Method 205
10.3.1 Cold Standby System 205
10.3.2 Warm Standby System 208
10.4 Approximation Method 211
10.4.1 Homogeneous Cold Standby System 212
10.4.2 Heterogeneous Cold Standby System 214
10.5 Event Transition Method 216
10.5.1 State-Space Representation of System Behavior 217
10.5.2 Basic Steps 218
10.5.3 Warm Standby System 218
10.6 Overview of Optimization Problems 220
10.7 Summary 222
References 222
Index 229
