Binary Decision Diagrams and Extensions for System Reliability Analysis

ISBN-13: 9781118549377 / Angielski / Twarda / 2015 / 240 str.

S. V. Amari

Opis

Recent advances in science and technology have made modern computing and engineering systems more powerful and sophisticated than ever. The increasing complexity and scale imply that system reliability problems not only continue to be a challenge but also require more efficient models and solutions. This is the first book systematically covering the state-of-the-art binary decision diagrams and their extended models, which can provide efficient and exact solutions to reliability analysis of large and complex systems. The book provides both basic concepts and detailed algorithms for modelling and evaluating reliability of a wide range of complex systems, such as multi-state systems, phased-mission systems, fault-tolerant systems with imperfect fault coverage, systems with common-cause failures, systems with disjoint failures, and systems with functional dependent failures. These types of systems abound in safety-critical or mission-critical applications such as aerospace, circuits, power systems, medical systems, telecommunication systems, transmission systems, traffic light systems, data storage systems, and etc. 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.

Spis treści

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