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Applied Reliability Engineering and Risk Analysis: Probabilistic Models and Statistical Inference

ISBN: 978-1-118-53942-2
448 pages
November 2013
Applied Reliability Engineering and Risk Analysis: Probabilistic Models and Statistical Inference (1118539427) cover image

Description

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.

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

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Table 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 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

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