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 Performability Design in the Twenty-First Century 119
Krishna B. Misra
9.1 Introduction 119
9.2 Strategies for Sustainable Development 120
9.3 Reappraisal of the Performance of Products and Systems 124
9.4 Dependability and Environmental Risk are Interdependent 126
9.5 Performability: An Appropriate Measure of Performance 126
9.6 Towards Dependable and Sustainable Designs 129
9.7 Conclusion 130
References 130
Part II NETWORKS AND LARGE-SCALE SYSTEMS
10 Network Reliability Calculations Based on Structural Invariants 135
Ilya B. Gertsbakh and Yoseph Shpungin
10.1 First Invariant: D-Spectrum, Signature 135
10.2 Second Invariant: Importance Spectrum. Birnbaum Importance Measure (BIM) 139
10.3 Example: Reliability of a Road Network 141
10.4 Third Invariant: Border States 142
10.5 Monte Carlo to Approximate the Invariants 144
10.6 Conclusion 146
References 146
11 Performance and Availability Evaluation of IMS-Based Core Networks 148
Kishor S. Trivedi, Fabio Postiglione and Xiaoyan Yin
11.1 Introduction 148
11.2 IMS-Based Core Network Description 149
11.3 Analytic Models for Independent Software Recovery 151
11.4 Analytic Models for Recovery with Dependencies 155
11.5 Redundancy Optimization 158
11.6 Numerical Results 159
11.7 Conclusion 165
References 165
12 Reliability and Probability of First Occurred Failure for Discrete-Time Semi-Markov Systems 167
Stylianos Georgiadis, Nikolaos Limnios and Irene Votsi
12.1 Introduction 167
12.2 Discrete-Time Semi-Markov Model 168
12.3 Reliability and Probability of First Occurred Failure 170
12.4 Nonparametric Estimation of Reliability Measures 172
12.5 Numerical Application 176
12.6 Conclusion 178
References 179
13 Single-Source Epidemic Process in a System of Two Interconnected Networks 180
Ilya B. Gertsbakh and Yoseph Shpungin
13.1 Introduction 180
13.2 Failure Process and the Distribution of the Number of Failed Nodes 181
13.3 Network Failure Probabilities 184
13.4 Example 185
13.5 Conclusion 187
13.A Appendix D: Spectrum (Signature) 188
References 189
Part III MAINTENANCE MODELS
14 Comparisons of Periodic and Random Replacement Policies 193
Xufeng Zhao and Toshio Nakagawa
14.1 Introduction 193
14.2 Four Policies 195
14.3 Comparisons of Optimal Policies 197
14.4 Numerical Examples 1 199
14.5 Comparisons of Policies with Different Replacement Costs 201
14.6 Numerical Examples 2 202
14.7 Conclusion 203
Acknowledgements 204
References 204
15 Random Evolution of Degradation and Occurrences of Words in Random Sequences of Letters 205
Emilio De Santis and Fabio Spizzichino
15.1 Introduction 205
15.2 Waiting Times to Words' Occurrences 206
15.3 Some Reliability-Maintenance Models 209
15.4 Waiting Times to Occurrences of Words and Stochastic Comparisons for Degradation 213
15.5 Conclusions 216
Acknowledgements 217
References 217
16 Occupancy Times for Markov and Semi-Markov Models in Systems Reliability 218
Alan G. Hawkes, Lirong Cui and Shijia Du
16.1 Introduction 218
16.2 Markov Models for Systems Reliability 220
16.3 Semi-Markov Models 222
16.4 Time Interval Omission 225
16.5 Numerical Examples 226
16.6 Conclusion 229
Acknowledgements 229
References 229
17 A Practice of Imperfect Maintenance Model Selection for Diesel Engines 231
Yu Liu, Hong-Zhong Huang, Shun-Peng Zhu and Yan-Feng Li
17.1 Introduction 231
17.2 Review of Imperfect Maintenance Model Selection Method 233
17.3 Application to Preventive Maintenance Scheduling of Diesel Engines 236
17.4 Conclusion 244
Acknowledgment 245
References 245
18 Reliability of Warm Standby Systems with Imperfect Fault Coverage 246
Rui Peng, Ola Tannous, Liudong Xing and Min Xie
18.1 Introduction 246
18.2 Literature Review 247
18.3 The BDD-Based Approach 250
18.4 Conclusion 253
Acknowledgments 254
References 254
Part IV STATISTICAL INFERENCE IN RELIABILITY
19 On the Validity of the Weibull-Gnedenko Model 259
Vilijandas Bagdonavi¡cius, Mikhail Nikulin and Ruta Levuliene
19.1 Introduction 259
19.2 Integrated Likelihood Ratio Test 261
19.3 Tests based on the Difference of Non-Parametric and Parametric Estimators of the Cumulative Distribution Function 264
19.4 Tests based on Spacings 266
19.5 Chi-Squared Tests 267
19.6 Correlation Test 269
19.7 Power Comparison 269
19.8 Conclusion 272
References 272
20 Statistical Inference for Heavy-Tailed Distributions in Reliability Systems 273
Ilia Vonta and Alex Karagrigoriou
20.1 Introduction 273
20.2 Heavy-Tailed Distributions 274
20.3 Examples of Heavy-Tailed Distributions 277
20.4 Divergence Measures 280
20.5 Hypothesis Testing 284
20.6 Simulations 286
20.7 Conclusion 287
References 287
21 Robust Inference based on Divergences in Reliability Systems 290
Abhik Ghosh, Avijit Maji and Ayanendranath Basu
21.1 Introduction 290
21.2 The Power Divergence (PD) Family 291
21.3 Density Power Divergence (DPD) and Parametric Inference 296
21.4 A Generalized Form: The S-Divergence 301
21.5 Applications 304
21.6 Conclusion 306
References 306
22 COM-Poisson Cure Rate Models and Associated Likelihood-based Inference with Exponential and Weibull Lifetimes 308
N. Balakrishnan and Suvra Pal
22.1 Introduction 308
22.2 Role of Cure Rate Models in Reliability 310
22.3 The COM-Poisson Cure Rate Model 310
22.4 Data and the Likelihood 311
22.5 EM Algorithm 312
22.6 Standard Errors and Asymptotic Confidence Intervals 314
22.7 Exponential Lifetime Distribution 314
22.8 Weibull Lifetime Distribution 322
22.9 Analysis of Cutaneous Melanoma Data 334
22.10 Conclusion 337
22.A1 Appendix A1: E-Step and M-Step Formulas for Exponential Lifetimes 337
22.A2 Appendix A2: E-Step and M-Step Formulas for Weibull Lifetimes 341
22.B1 Appendix B1: Observed Information Matrix for Exponential Lifetimes 344
22.B2 Appendix B2: Observed Information Matrix for Weibull Lifetimes 346
References 347
23 Exponential Expansions for Perturbed Discrete Time Renewal Equations 349
Dmitrii Silvestrov and Mikael Petersson
23.1 Introduction 349
23.2 Asymptotic Results 350
23.3 Proofs 353
23.4 Discrete Time Regenerative Processes 358
23.5 Queuing and Risk Applications 359
References 361
24 On Generalized Extreme Shock Models under Renewal Shock Processes 363
Ji Hwan Cha and Maxim Finkelstein
24.1 Introduction 363
24.2 Generalized Extreme Shock Models 364
24.3 Specific Models 367
24.4 Conclusion 373
Acknowledgements 373
References 373
Part V SYSTEMABILITY, PHYSICS-OF-FAILURE AND RELIABILITY DEMONSTRATION
25 Systemability Theory and its Applications 377
Hoang Pham
25.1 Introduction 377
25.2 Systemability Measures 378
25.3 Systemability Analysis of k-out-of-n Systems 379
25.4 Systemability Function Approximation 380
25.5 Systemability with Loglog Distribution 383
25.6 Sensitivity Analysis 384
25.7 Applications: Red Light Camera Systems 385
25.8 Conclusion 387
References 387
26 Physics-of-Failure based Reliability Engineering 389
Pedro O. Quintero and Michael Pecht
26.1 Introduction 389
26.2 Physics-of-Failure-based Reliability Assessment 393
26.3 Uses of Physics-of-Failure 398
26.4 Conclusion 400
References 400
27 Accelerated Testing: Effect of Variance in Field Environmental Conditions on the Demonstrated Reliability 403
Andre Kleyner
27.1 Introduction 403
27.2 Accelerated Testing and Field Stress Variation 404
27.3 Case Study: Reliability Demonstration Using Temperature Cycling Test 405
27.4 Conclusion 408
References 408
Index 409
