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"This book presents the latest developments in the field of reliability science focusing on applied reliability, probabilistic models and risk analysis. It provides readers with the most up-to-date developments in this field and consolidates research activities in several areas of applied reliability engineering. The publication is timed to commemorate Boris Gnedenko's centennial by bringing together leading researchers, scientists, and practitioners in the field of Prof. Gnednko's expertise. The Introduction, written by Prof. Igor Ushakov, a personal friend and a colleague of Boris Gnedenko, explains the significant impact and contribution Gnedenko's work made on the reliability theory and the modern reliability practice. The book covers conventional and contemporary (recently emerged) topics in reliability science, which have seen extended research activities in the recent years. These topics include: degradation analysis and multi-state system reliability; networks and large scale systems; maintenance models; statistical inference in reliability, and; physics of failures and reliability demonstration. All of these topics present a great interest to researchers and practitioners, having been extensively researched in the past years and covered at a large number of international conferences and in a multitude of journal articles. This book pulls together this information with a coherent flow of chapters, and is written by the lead scientists, researchers and practitioners in their respective fields. Logically divided into five sections, each contains several chapters covering theoretical and practical issues, while case studies support the topics under discussion"--
List of contents
Remembering Boris Gnedenko xvii
List of Contributors xxv
Preface xxix
Acknowledgements xxxv
Part I DEGRADATION ANALYSIS, MULTI-STATE AND CONTINUOUS-STATE SYSTEM RELIABILITY
1 Methods of Solutions of Inhomogeneous Continuous Time Markov Chains for Degradation Process Modeling 3
Yan-Fu Li, Enrico Zio and Yan-Hui Lin
1.1 Introduction 3
1.2 Formalism of ICTMC 4
1.3 Numerical Solution Techniques 5
1.4 Examples 10
1.5 Comparisons of the Methods and Guidelines of Utilization 13
1.6 Conclusion 15
References 15
2 Multistate Degradation and Condition Monitoring for Devices with Multiple Independent Failure Modes 17
Ramin Moghaddass and Ming J. Zuo
2.1 Introduction 17
2.2 Multistate Degradation and Multiple Independent Failure Modes 19
2.3 Parameter Estimation 23
2.4 Important Reliability Measures of a Condition-Monitored Device 25
2.5 Numerical Example 27
2.6 Conclusion 28
Acknowledgements 30
References 30
3 Time Series Regression with Exponential Errors for Accelerated Testing and Degradation Tracking 32
Nozer D. Singpurwalla
3.1 Introduction 32
3.2 Preliminaries: Statement of the Problem 33
3.3 Estimation and Prediction by Least Squares 34
3.4 Estimation and Prediction by MLE 35
3.5 The Bayesian Approach: The Predictive Distribution 37
Acknowledgements 42
References 42
4 Inverse Lz-Transform for a Discrete-State Continuous-Time Markov Process and Its Application to Multi-State System Reliability Analysis 43
Anatoly Lisnianski and Yi Ding
4.1 Introduction 43
4.2 Inverse Lz-Transform: Definitions and Computational Procedure 44
4.3 Application of Inverse Lz-Transform to MSS Reliability Analysis 50
4.4 Numerical Example 52
4.5 Conclusion 57
References 58
5 OntheLz-Transform Application for Availability Assessment of an Aging Multi-State Water Cooling System for Medical Equipment 59
Ilia Frenkel, Anatoly Lisnianski and Lev Khvatskin
5.1 Introduction 59
5.2 Brief Description of the Lz-Transform Method 61
5.3 Multi-state Model of the Water Cooling System for the MRI Equipment 62
5.4 Availability Calculation 75
5.5 Conclusion 76
Acknowledgments 76
References 77
6 Combined Clustering and Lz-Transform Technique to Reduce the Computational Complexity of a Multi-State System Reliability Evaluation 78
Yi Ding
6.1 Introduction 78
6.2 The Lz-Transform for Dynamic Reliability Evaluation for MSS 79
6.3 Clustering Composition Operator in the Lz-Transform 81
6.4 Computational Procedures 83
6.5 Numerical Example 83
6.6 Conclusion 85
References 85
7 Sliding Window Systems with Gaps 87
Gregory Levitin
7.1 Introduction 87
7.2 The Models 89
7.3 Reliability Evaluation Technique 91
7.4 Conclusion 96
References 96
8 Development of Reliability Measures Motivated by Fuzzy Sets for Systems with Multi- or Infinite-States 98
Zhaojun (Steven) Li and Kailash C. Kapur
8.1 Introduction 98
8.2 Models for Components and Systems Using Fuzzy Sets 100
8.3 Fuzzy Reliability for Systems with Continuous or Infinite States 103
8.4 Dynamic Fuzzy Reliability 104
8.5 System Fuzzy Reliability 110
8.6 Examples and Applications 111
8.7 Conclusion 117
References 118
9 Imperatives for Perform
