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This book offers a comprehensive overview of recently developed methods for assessing and optimizing system reliability. It consists of two main parts, for treating assessment methods and optimization methods, respectively.
The first part covers methods of multi-state system reliability modelling and evaluation, Markov processes, Monte Carlo simulation and uncertainty analysis. The methods considered range from piecewise-deterministic Markov processes to belief function analysis. The second part covers optimization methods of mathematical programming and evolutionary algorithms, and problems of multi-objective optimization and optimization under uncertainty. The methods of this part range from non-dominated sorting genetic algorithm to robust optimization.
The book also includes the application of the assessment and optimization methods considered on real case studies, particularly with respect to the reliability assessment and optimization of renewable energy systems, and bridges the gap between theoretical method development and engineering practice.
List of contents
Series Editor's Foreword by Dr. Andre V. Kleyner xv
Preface xvii
Acknowledgments xix
List of Abbreviations xx
Notations xxii
Part I The Fundamentals 1
1 Reliability Assessment 3
1.1 Definitions of Reliability 3
1.1.1 Probability of Survival 3
1.2 Component Reliability Modeling 6
1.2.1 Discrete Probability Distributions 6
1.2.2 Continuous Probability Distributions 8
1.2.3 Physics-of-Failure Equations 13
1.3 System Reliability Modeling 15
1.3.1 Series System 15
1.3.2 Parallel System 16
1.3.3 Series-parallel System 16
1.3.4 K-out-of-n System 17
1.3.5 Network System 18
1.4 System Reliability Assessment Methods 18
1.4.1 Path-set and Cut-set Method 18
1.4.2 Decomposition and Factorization 19
1.4.3 Binary Decision Diagram 19
1.5 Exercises 20
References 22
2 Optimization 23
2.1 Optimization Problems 23
2.1.1 Component Reliability Enhancement 23
2.1.2 Redundancy Allocation 24
2.1.3 Component Assignment 25
2.1.4 Maintenance and Testing 26
2.2 Optimization Methods 30
2.2.1 Mathematical Programming 30
2.2.2 Meta-heuristics 34
2.3 Exercises 36
References 37
Part II Reliability Techniques 41
3 Multi-State Systems (MSSs) 43
3.1 Classical Multi-state Models 43
3.2 Generalized Multi-state Models 45
3.3 Time-dependent Multi-State Models 46
3.4 Methods to Evaluate Multi-state System Reliability 48
3.4.1 Methods Based on MPVs or MCVs 48
3.4.2 Methods Derived from Binary State Reliability Assessment 48
3.4.3 Universal Generating Function Approach 49
3.4.4 Monte Carlo Simulation 50
3.5 Exercises 51
References 51
4 Markov Processes 55
4.1 Continuous Time Markov Chain (CMTC) 55
4.2 In homogeneous Continuous Time Markov Chain 61
4.3 Semi-Markov Process (SMP) 66
4.4 Piecewise Deterministic Markov Process (PDMP) 74
4.5 Exercises 82
References 84
5 Monte Carlo Simulation (MCS) for Reliability and Availability Assessment 87
5.1 Introduction 87
5.2 Random Variable Generation 87
5.2.1 Random Number Generation 87
5.2.2 Random Variable Generation 89
5.3 Random Process Generation 93
5.3.1 Markov Chains 93
5.3.2 Markov Jump Processes 94
5.4 Markov Chain Monte Carlo (MCMC) 97
5.4.1 Metropolis-Hastings (M-H) Algorithm 97
5.4.2 Gibbs Sampler 98
5.4.3 Multiple-try Metropolis-Hastings (M-H) Method 99
5.5 Rare-Event Simulation 101
5.5.1 Importance Sampling 101
5.5.2 Repetitive Simulation Trials after Reaching Thresholds (RESTART) 102
5.6 Exercises 103
Appendix 104
References 115
6 Uncertainty Treatment under Imprecise or Incomplete Knowledge 117
6.1 Interval Number and Interval of Confidence 117
6.1.1 Definition and Basic Arithmetic Operations 117
6.1.2 Algebraic Properties 118
6.1.3 Order Relations 119
6.1.4 Interval Functions 120
6.1.5 Interval of Confidence 121
6.2 Fuzzy Number 121
6.3 Possibility Theory 123
6.3.1 Possibility Propagation 124
6.4 Evidence Theory 125
6.4.1 Data Fusion 128
6.5 Random-fuzzy Numbers (RFNs) 128
6.5.1 Universal Generating Function (UGF) Repr
About the author
Yan-Fu Li is Full Professor at the Department of Industrial Engineering and the Director of the Institute for Quality & Reliability at Tsinghua University, China. He received his Ph.D in Industrial Engineering from National University of Singapore in 2010
Enrico Zio is Full Professor at Mines-Paris, PSL University, and at the Energy Department of Politecnico di Milano, Italy. He received his Ph.D in nuclear engineering from Politecnico di Milano and in Probabilistic Risk Assessment from MIT in 1996 and 1998, respectively.
