Applied Reliability Engineering and Risk Analysis Probabilistic Models and Statistical Inference
, by Frenkel, Ilia B.; Karagrigoriou, Alex; Lisnianski, Anatoly; Kleyner, Andre
- ISBN: 9781118539422 | 1118539427
- Cover: Hardcover
- Copyright: 11/11/2013
This complete resource on the theory and applications of reliability engineering, probabilistic models and risk analysis consolidates all the latest research, presenting the most up-to-date developments in this field.
With comprehensive coverage of the theoretical and practical issues of both classic and modern topics, it also provides a unique commemoration to the centennial of the birth of Boris Gnedenko, one of the most prominent reliability scientists of the twentieth century.
With comprehensive coverage of the theoretical and practical issues of both classic and modern topics, it also provides a unique commemoration to the centennial of the birth of Boris Gnedenko, one of the most prominent reliability scientists of the twentieth century.
Key features include:
- expert treatment of probabilistic models and statistical inference from leading scientists, researchers and practitioners in their respective reliability fields
- detailed coverage of multi-state system reliability, maintenance models, statistical inference in reliability, systemability, physics of failures and reliability demonstration
- many examples and engineering case studies to illustrate the theoretical results and their practical applications in industry
Applied Reliability Engineering and Risk Analysis is one of the first works to treat the important areas of degradation analysis, multi-state system reliability, networks and large-scale systems in one comprehensive volume. It is an essential reference for engineers and scientists involved in reliability analysis, applied probability and statistics, reliability engineering and maintenance, logistics, and quality control. It is also a useful resource for graduate students specialising in reliability analysis and applied probability and statistics.
Dedicated to the Centennial of the birth of Boris Gnedenko, renowned Russian mathematician and reliability theorist
Ilia Frenkel, Center for Reliability and Risk Management, Industrial Engineering and Management Department, SCE - Shamoon College of Engineering, Israel
Ilia has forty years academic experience, teaching in Russia and Israel. Currently he is a senior lecturer and Director of the Centre for Reliability and Risk Management in the Industrial Engineering and Management Department of the SCE - Shamoon College of Engineering, Israel. Previously he worked as Department Chair and Associate Professor in the Applied Mathematics and Computers Department at Volgograd Civil Engineering Institute. He is a member of the editorial board on Maintenance and Reliability, Communications in Dependability and Quality Management, and has published scientific articles and book chapters in the fields of reliability, applied statistics and production and operation management.
Alex Karagrigoriou, Department of Mathematics and Statistics, University of Cyprus
Alex is Associate Professor of Statistics, Department of Mathematics and Statistics, University of Cyprus and Professor of Probability and Statistics, University of the Aegean. He worked at the University of Maryland, the United States Department of Agriculture and the Institute of Statistical Sciences, Taiwan, and taught thirty-two courses at the Universities of Maryland, Athens, the Aegean, and Cyprus. He has been involved in the organization of eight international conferences. He has written two textbooks on statistical analysis, teaching notes for undergraduate and graduate courses, and has published more than fifty articles on statistics and applied probability. Alex has served as reviewer for the United States National Security Council and the United Kingdom Economic and Social Research Council.
Anatoly Lisnianski, Reliability Department, The Israel Electric Corporation Ltd., Israel
Anatoly is an engineering expert in the Reliability Department of The Israel Electric Corporation Ltd., Israel, an adjunct senior lecturer in Haifa University, Israel, and Scientific Supervisor of the Centre for Reliability and Risk Management in the Industrial Engineering and Management Department of the SCE - Shamoon College of Engineering, Israel. Previous to this he was Senior Researcher in Federal Scientific & Production Center "Aurora" in St-Petersburg, Russia. He is a Senior Member of IEEE, Member of Israel Society of Quality and Israel Statistical Association, and is an author of more than one hundred publications in the field of reliability and applied probability.
He has been guest editor for International Journal of Reliability, Quality and Safety Engineering.
Andre Kleyner, Global Reliability Engineering Leader, Delphi Electronics and Safety, USA
Andre has twenty-five years of engineering, research, consulting, and managerial experience specializing in the reliability of electronic and mechanical systems. He is currently a Global Reliability Engineering Leader with Delphi Electronics & Safety and an adjunct professor at Purdue University.? He is a senior member of American Society for Quality, a Certified Reliability Engineer, Certified Quality Engineer, and a Six Sigma Black Belt.? He also holds several US and foreign patents and authored multiple publications on the topics of reliability, statistics, warranty management, and lifecycle cost analysis.? Andre Kleyner is Editor of the Wiley Series in Quality & Reliability Engineering.
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
1.3.1 The Runge–Kutta Method 5
1.3.2 Uniformization 6
1.3.3 Monte Carlo Simulation 7
1.3.4 State-Space Enrichment 9
1.4 Examples 10
1.4.1 Example of Computing System Degradation 10
1.4.2 Example of Nuclear Component Degradation 11
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
2.2.1 Notation 19
2.2.2 Assumptions 20
2.2.3 The Stochastic Process Model 21
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
3.2.1 Relevance to Accelerated Testing, Degradation and Risk 33
3.3 Estimation and Prediction by Least Squares 34
3.4 Estimation and Prediction by MLE 35
3.4.1 Properties of the Maximum Likelihood Estimator 35
3.5 The Bayesian Approach: The Predictive Distribution 37
3.5.1 The Predictive Distribution of YT+1 when λ > A 38
3.5.2 The Predictive Distribution of YT+1 when λ ≤ A 39
3.5.3 Alternative Prior for β 40
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
4.2.1 Definitions 44
4.2.2 Computational Procedure 47
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
5.3.1 System Description 62
5.3.2 The Chiller Sub-System 64
5.3.3 The Heat Exchanger Sub-System 66
5.3.4 The Pump Sub-System 67
5.3.5 The Electric Board Sub-System 69
5.3.6 Model of Stochastic Demand 71
5.3.7 Multi-State Model for the MRI Cooling System 73
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
7.2.1 The k/eSWS Model 89
7.2.2 The mCSWS Model 89
7.2.3 The mGSWS Model 90
7.2.4 Interrelations among Different Models 90
7.3 Reliability Evaluation Technique 91
7.3.1 Determining u-functions for Individual Elements and their Groups 91
7.3.2 Determining u-functions for all the Groups of r Consecutive Elements 92
7.3.3 Detecting the System Failure 93
7.3.4 Updating the Counter 94
7.3.5 Recursive Determination of System Failure Probability 95
7.3.6 Computational Complexity Reduction 95
7.3.7 Algorithm for System Reliability Evaluation 95
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
8.2.1 Binary Reliability and Multi-State Reliability Model 100
8.2.2 Definition of Fuzzy Reliability 101
8.2.3 Fuzzy Unreliability: A Different Perspective 102
8.2.4 Evolution from Binary State to Multi-State and to Fuzzy State Reliability Modeling 102
8.3 Fuzzy Reliability for Systems with Continuous or Infinite States 103
8.4 Dynamic Fuzzy Reliability 104
8.4.1 Time to Fuzzy Failure Modeled by Fuzzy Random Variable 105
8.4.2 Stochastic Performance Degradation Model 106
8.4.3 Membership Function Evaluation for the Expectation of Time to Fuzzy Failure 107
8.4.4 Performance Measures for Dynamic Fuzzy Reliability 108
8.5 System Fuzzy Reliability 110
8.6 Examples and Applications 111
8.6.1 Reliability Performance Evaluation Based on Time to Fuzzy Failure 111
8.6.2 Example for System Fuzzy Reliability Modeling 113
8.6.3 Numerical Results 115
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
9.2.1 The Internalization of Hidden Costs 120
9.2.2 Mitigation Policies 121
9.2.3 Dematerialization 121
9.2.4 Minimization of Energy Requirement 124
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
9.5.1 Performability Engineering 127
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
11.3.1 Model 1: Hierarchical Model with Top-Level RBD and Lower-Level MFT 152
11.3.2 Model 2: Hierarchical Model with Top-Level RBD and Lower-Level FT 153
11.3.3 Model 3: Hierarchical Model with Top-Level RBD and Lower-Level SRN 154
11.4 Analytic Models for Recovery with Dependencies 155
11.4.1 Model 4: Hierarchical Model with Top-Level RBD, Middle-Level MFT and Lower-Level CTMC 155
11.4.2 Model 5: Alternative Approach for Model 4 based on UGF 156
11.4.3 Model 6: Hierarchical Model with Top-Level RBD and Lower-Level SRN 158
11.5 Redundancy Optimization 158
11.6 Numerical Results 159
11.6.1 Model Comparison 159
11.6.2 Influences of Performance Demand and Redundancy Configuration 162
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
12.3.1 Rate of Occurrence of Failures 171
12.3.2 Steady-State Availability 171
12.3.3 Probability of First Occurred Failure 172
12.4 Nonparametric Estimation of Reliability Measures 172
12.4.1 Estimation of ROCOF 173
12.4.2 Estimation of the Steady-State Availability 174
12.4.3 Estimation of the Probability of First Occurred Failure 175
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
14.2.1 Standard Replacement 195
14.2.2 Replacement First 195
14.2.3 Replacement Last 196
14.2.4 Replacement Over Time 196
14.3 Comparisons of Optimal Policies 197
14.3.1 Comparisons of T ∗ S and T ∗ F, T ∗ L, and T ∗ O 197
14.3.2 Comparisons of T ∗ O and T ∗ F, T ∗ L 198
14.3.3 Comparisons of T ∗ F and T ∗ L 199
14.4 Numerical Examples 1 199
14.5 Comparisons of Policies with Different Replacement Costs 201
14.5.1 Comparisons of T ∗ S, and T ∗ F, T ∗ L 201
14.5.2 Comparisons of T ∗ S and T ∗ O 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
15.2.1 The Markov Chain Approach 207
15.2.2 Leading Numbers and Occurrences Times 208
15.3 Some Reliability-Maintenance Models 209
15.3.1 Model 1 (Simple Machine Replacement) 209
15.3.2 Model 2 (Random Reduction of Age) 210
15.3.3 Model 3 (Random Number of Effective Repairs in a Parallel System) 211
15.3.4 Degradation and Words 212
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
16.3.1 Joint Distributions of Operational and Failed Times 223
16.3.2 Distribution of Cumulative Times 224
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
17.2.1 Estimation of the Parameters 234
17.2.2 The Proposed GOF Test 234
17.2.3 Bayesian Model Selection 235
17.3 Application to Preventive Maintenance Scheduling of Diesel Engines 236
17.3.1 Initial Failure Intensity Estimation 237
17.3.2 Imperfect Maintenance Model Selection 237
17.3.3 Implementation in Preventive Maintenance Decision-Making 240
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
18.3.1 The BDD Construction 251
18.3.2 System Unreliability Evaluation 251
18.3.3 Illustrative Examples 252
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
21.2.1 Minimum Disparity Estimation 293
21.2.2 The Robustness of the Minimum Disparity Estimators (MDEs) 294
21.2.3 Asymptotic Properties 295
21.3 Density Power Divergence (DPD) and Parametric Inference 296
21.3.1 Connections between the PD and the DPD 298
21.3.2 Influence Function of the Minimum DPD estimator 299
21.3.3 Asymptotic Properties of the Minimum DPD estimator 300
21.4 A Generalized Form: The S-Divergence 301
21.4.1 The Divergence and the Estimating Equation 301
21.4.2 Influence Function of the Minimum S-Divergence estimator 303
21.4.3 Minimum S-Divergence Estimators: Asymptotic Properties 303
21.5 Applications 304
21.5.1 Reliability: The Generalized Pareto Distribution 304
21.5.2 Survival Analysis 305
21.5.3 Model Selection: Divergence Information Criterion 306
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
22.7.1 Simulation Study: Model Fitting 315
22.7.2 Simulation Study: Model Discrimination 319
22.8 Weibull Lifetime Distribution 322
22.8.1 Simulation Study: Model Fitting 322
22.8.2 Simulation Study: Model Discrimination 328
22.9 Analysis of Cutaneous Melanoma Data 334
22.9.1 Exponential Lifetimes with Log-Linear Link Function 334
22.9.2 Weibull Lifetimes with Logistic Link Function 335
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
24.2.1 ‘Classical’ Extreme Shock Model for Renewal Process of Shocks 364
24.2.2 History-Dependent Extreme Shock Model 365
24.3 Specific Models 367
24.3.1 Stress-Strength Model 367
24.3.2 Model A in Cha and Finkelstein (2011) 369
24.3.3 State-Dependent Shock Model 370
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
25.3.1 Variance of Systemability Calculations 380
25.4 Systemability Function Approximation 380
25.5 Systemability with Loglog Distribution 383
25.5.1 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
26.2.1 Information Requirements 393
26.2.2 Failure Modes, Mechanisms, and Effects Analysis (FMMEA) 396
26.2.3 Stress Analysis 397
26.2.4 Reliability Assessment 397
26.3 Uses of Physics-of-Failure 398
26.3.1 Design-for-Reliability (DfR) 398
26.3.2 Stress Testing Conditions 398
26.3.3 Qualification 399
26.3.4 Screening Conditions 399
26.3.5 Prognostics and Health Management (PHM) 399
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
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