Dynamic System Reliability Modeling and Analysis of Dynamic and Dependent Behaviors

Offers timely and comprehensive coverage of dynamic system reliability theory

This book focuses on hot issues of dynamic system reliability, systematically introducing the reliability modeling and analysis methods for systems with imperfect fault coverage, systems with function dependence, systems subject to deterministic or probabilistic common-cause failures, systems subject to deterministic or probabilistic competing failures, and dynamic standby sparing systems. It presents recent developments of such extensions involving reliability modelling theory, reliability evaluation methods, and features numerous case studies based on real-world examples. The presented dynamic reliability theory can enable a more accurate representation of actual complex system behavior, thus more effectively guiding the reliable design of real-world critical systems.

Dynamic System Reliability: Modelling and Analysis of Dynamic and Dependent Behaviors begins by describing the evolution from the traditional static reliability theory to the dynamic system reliability theory, and provides a detailed investigation of dynamic and dependent behaviors in subsequent chapters. Although written for those with a background in basic probability theory and stochastic processes, the book includes a chapter reviewing the fundamentals that readers need to know in order to understand contents of other chapters which cover advanced topics in reliability theory and case studies. 

• The first book systematically focusing on dynamic system reliability modelling and analysis theory
• Provides a comprehensive treatment on imperfect fault coverage (single-level/multi-level or modular), function dependence, common cause failures (deterministic and probabilistic), competing failures (deterministic and probabilistic), and dynamic standby sparing
• Includes abundant illustrative examples and case studies based on real-world systems
• Covers recent advances in combinatorial models and algorithms for dynamic system reliability analysis
• Offers a rich set of references, providing helpful resources for readers to pursue further research and study of the topics

Dynamic System Reliability: Modelling and Analysis of Dynamic and Dependent Behaviors is an excellent book for undergraduate and graduate students, and engineers and researchers in reliability and related disciplines. 

Liudong Xing, PhD, is a Full Professor in the Department of Electrical and Computer Engineering at University of Massachusetts (UMass) Dartmouth, USA.

Gregory Levitin, PhD, is a senior expert in the Reliability Department at The Israel Electric Corporation, Israel, and a distinguished visiting professor at University of Electronic Science and Technology of China. 

Chaonan Wang, PhD, is a Full Professor at the College of Information Science and Technology at Jinan University, Guangzhou, China.

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

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