Binary Decision Diagrams and Extensions for System Reliability Analysis

The book provides both small-scale illustrative examples and large-scale benchmark examples to demonstrate broad applications and advantages of different decision diagrams based methods for complex system reliability analysis. Other measures including component importance and failure frequency are also covered. A rich set of references is cited in the book, providing helpful resources for readers to pursue further research and study of the topics. The target audience of the book is reliability and safety engineers or researchers.

The book can serve as a textbook on system reliability analysis. It can also serve as a tutorial and reference book on decision diagrams, multi-state systems, phased-mission systems, and imperfect fault coverage models.

Liudong Xing is a tenured professor in the Department of Electrical and Computer Engineering at the University of Massachusetts (UMass), Dartmouth. She received her PhD degree in Electrical Engineering from the University of Virginia, Charlottesville in 2002. Her current research focuses on reliability modelling and analysis of complex systems and networks. She has authored or co-authored over 190 technical papers. She is the recipient of the Leo M. Sullivan Teacher of the Year Award (2014), Scholar of the Year Award (2010), and Outstanding Women Award (2011) of UMass Dartmouth, as well as the IEEE Region 1 Technological Innovation (Academic) Award (2007). She is also the co-recipient of the Best Paper Award at the IEEE International Conference on Networking, Architecture, and Storage in 2009. She is a senior member of IEEE.

Suprasad V. Amari received the M.S. and Ph.D. degrees in Reliability Engineering from the Indian Institute of Technology, Kharagpur, India. He is a senior technical staff member at Relyence Corporation. Prior to joining Relyence, he has served as a Technical Fellow at Parametric Technology Corporation (PTC) for 14 years, where he was responsible for research, design, and development of PTC's reliability modeling and analysis software products. He has authored or coauthored 6 book chapters in Springer Handbooks and about 90 technical papers in the area of reliability engineering. He has been actively involved with Annual Reliability and Maintainability Symposium (RAMS) and currently serving as the Vice General Chair. He has received the 2013 RAMS Best Paper Award from American Society for Quality (ASQ) Reliability Division, the 2009 Stan Oftshun Award from the Society of Reliability Engineers (SRE) and the 2009 William A.J. Golomski Award from the Institute of Industrial Engineers (IIE). He is a senior member of ASQ, IEEE, and IIE. He is a member of ACM, SAE and SRE and an ASQ-certified Reliability Engineer.

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

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