Applied Reliability Engineering and Risk Analysis

Ilia Frenkel, Center for Reliability and Risk Management, Industrial Engineering and Management Department, SCE - Shamoon College of Engineering, IsraelIlia 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 CyprusAlex 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., IsraelAnatoly 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, USAAndre 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.

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• Remembering Boris Gnedenko xvii List of Contributors xxvPreface xxixAcknowledgements xxxvPart I DEGRADATION ANALYSIS, MULTI-STATE AND CONTINUOUS-STATE SYSTEM RELIABILITY1 Methods of Solutions of Inhomogeneous Continuous Time Markov Chains for Degradation Process Modeling 3Yan-Fu Li, Enrico Zio and Yan-Hui Lin1.1 Introduction 31.2 Formalism of ICTMC 41.3 Numerical Solution Techniques 51.4 Examples 101.5 Comparisons of the Methods and Guidelines of Utilization 131.6 Conclusion 15References 152 Multistate Degradation and Condition Monitoring for Devices with Multiple Independent Failure Modes 17Ramin Moghaddass and Ming J. Zuo2.1 Introduction 172.2 Multistate Degradation and Multiple Independent Failure Modes 192.3 Parameter Estimation 232.4 Important Reliability Measures of a Condition-Monitored Device 252.5 Numerical Example 272.6 Conclusion 28Acknowledgements 30References 303 Time Series Regression with Exponential Errors for Accelerated Testing and Degradation Tracking 32Nozer D. Singpurwalla3.1 Introduction 323.2 Preliminaries: Statement of the Problem 333.3 Estimation and Prediction by Least Squares 343.4 Estimation and Prediction by MLE 353.5 The Bayesian Approach: The Predictive Distribution 37Acknowledgements 42References 424 Inverse Lz-Transform for a Discrete-State Continuous-Time Markov Process and Its Application to Multi-State System Reliability Analysis 43Anatoly Lisnianski and Yi Ding4.1 Introduction 434.2 Inverse Lz-Transform: Definitions and Computational Procedure 444.3 Application of Inverse Lz-Transform to MSS Reliability Analysis 504.4 Numerical Example 524.5 Conclusion 57References 585 OntheLz-Transform Application for Availability Assessment of an Aging Multi-State Water Cooling System for Medical Equipment 59Ilia Frenkel, Anatoly Lisnianski and Lev Khvatskin5.1 Introduction 595.2 Brief Description of the Lz-Transform Method 615.3 Multi-state Model of the Water Cooling System for the MRI Equipment 625.4 Availability Calculation 755.5 Conclusion 76Acknowledgments 76References 776 Combined Clustering and Lz-Transform Technique to Reduce the Computational Complexity of a Multi-State System Reliability Evaluation 78Yi Ding6.1 Introduction 786.2 The Lz-Transform for Dynamic Reliability Evaluation for MSS 796.3 Clustering Composition Operator in the Lz-Transform 816.4 Computational Procedures 836.5 Numerical Example 836.6 Conclusion 85References 857 Sliding Window Systems with Gaps 87Gregory Levitin7.1 Introduction 877.2 The Models 897.3 Reliability Evaluation Technique 917.4 Conclusion 96References 968 Development of Reliability Measures Motivated by Fuzzy Sets for Systems with Multi- or Infinite-States 98Zhaojun (Steven) Li and Kailash C. Kapur8.1 Introduction 988.2 Models for Components and Systems Using Fuzzy Sets 1008.3 Fuzzy Reliability for Systems with Continuous or Infinite States 1038.4 Dynamic Fuzzy Reliability 1048.5 System Fuzzy Reliability 1108.6 Examples and Applications 1118.7 Conclusion 117References 1189 Imperatives for Performability Design in the Twenty-First Century 119Krishna B. Misra9.1 Introduction 1199.2 Strategies for Sustainable Development 1209.3 Reappraisal of the Performance of Products and Systems 1249.4 Dependability and Environmental Risk are Interdependent 1269.5 Performability: An Appropriate Measure of Performance 1269.6 Towards Dependable and Sustainable Designs 1299.7 Conclusion 130References 130Part II NETWORKS AND LARGE-SCALE SYSTEMS10 Network Reliability Calculations Based on Structural Invariants 135Ilya B. Gertsbakh and Yoseph Shpungin10.1 First Invariant: D-Spectrum, Signature 13510.2 Second Invariant: Importance Spectrum. Birnbaum Importance Measure (BIM) 13910.3 Example: Reliability of a Road Network 14110.4 Third Invariant: Border States 14210.5 Monte Carlo to Approximate the Invariants 14410.6 Conclusion 146References 14611 Performance and Availability Evaluation of IMS-Based Core Networks 148Kishor S. Trivedi, Fabio Postiglione and Xiaoyan Yin11.1 Introduction 14811.2 IMS-Based Core Network Description 14911.3 Analytic Models for Independent Software Recovery 15111.4 Analytic Models for Recovery with Dependencies 15511.5 Redundancy Optimization 15811.6 Numerical Results 15911.7 Conclusion 165References 16512 Reliability and Probability of First Occurred Failure for Discrete-Time Semi-Markov Systems 167Stylianos Georgiadis, Nikolaos Limnios and Irene Votsi12.1 Introduction 16712.2 Discrete-Time Semi-Markov Model 16812.3 Reliability and Probability of First Occurred Failure 17012.4 Nonparametric Estimation of Reliability Measures 17212.5 Numerical Application 17612.6 Conclusion 178References 17913 Single-Source Epidemic Process in a System of Two Interconnected Networks 180Ilya B. Gertsbakh and Yoseph Shpungin13.1 Introduction 18013.2 Failure Process and the Distribution of the Number of Failed Nodes 18113.3 Network Failure Probabilities 18413.4 Example 18513.5 Conclusion 18713.A Appendix D: Spectrum (Signature) 188References 189Part III MAINTENANCE MODELS14 Comparisons of Periodic and Random Replacement Policies 193Xufeng Zhao and Toshio Nakagawa14.1 Introduction 19314.2 Four Policies 19514.3 Comparisons of Optimal Policies 19714.4 Numerical Examples 1 19914.5 Comparisons of Policies with Different Replacement Costs 20114.6 Numerical Examples 2 20214.7 Conclusion 203Acknowledgements 204References 20415 Random Evolution of Degradation and Occurrences of Words in Random Sequences of Letters 205Emilio De Santis and Fabio Spizzichino15.1 Introduction 20515.2 Waiting Times to Words’ Occurrences 20615.3 Some Reliability-Maintenance Models 20915.4 Waiting Times to Occurrences of Words and Stochastic Comparisons for Degradation 21315.5 Conclusions 216Acknowledgements 217References 21716 Occupancy Times for Markov and Semi-Markov Models in Systems Reliability 218Alan G. Hawkes, Lirong Cui and Shijia Du16.1 Introduction 21816.2 Markov Models for Systems Reliability 22016.3 Semi-Markov Models 22216.4 Time Interval Omission 22516.5 Numerical Examples 22616.6 Conclusion 229Acknowledgements 229References 22917 A Practice of Imperfect Maintenance Model Selection for Diesel Engines 231Yu Liu, Hong-Zhong Huang, Shun-Peng Zhu and Yan-Feng Li17.1 Introduction 23117.2 Review of Imperfect Maintenance Model Selection Method 23317.3 Application to Preventive Maintenance Scheduling of Diesel Engines 23617.4 Conclusion 244Acknowledgment 245References 24518 Reliability of Warm Standby Systems with Imperfect Fault Coverage 246Rui Peng, Ola Tannous, Liudong Xing and Min Xie18.1 Introduction 24618.2 Literature Review 24718.3 The BDD-Based Approach 25018.4 Conclusion 253Acknowledgments 254References 254Part IV STATISTICAL INFERENCE IN RELIABILITY19 On the Validity of the Weibull-Gnedenko Model 259Vilijandas Bagdonavi¡cius, Mikhail Nikulin and Ruta Levuliene19.1 Introduction 25919.2 Integrated Likelihood Ratio Test 26119.3 Tests based on the Difference of Non-Parametric and Parametric Estimators of the Cumulative Distribution Function 26419.4 Tests based on Spacings 26619.5 Chi-Squared Tests 26719.6 Correlation Test 26919.7 Power Comparison 26919.8 Conclusion 272References 27220 Statistical Inference for Heavy-Tailed Distributions in Reliability Systems 273Ilia Vonta and Alex Karagrigoriou20.1 Introduction 27320.2 Heavy-Tailed Distributions 27420.3 Examples of Heavy-Tailed Distributions 27720.4 Divergence Measures 28020.5 Hypothesis Testing 28420.6 Simulations 28620.7 Conclusion 287References 28721 Robust Inference based on Divergences in Reliability Systems 290Abhik Ghosh, Avijit Maji and Ayanendranath Basu21.1 Introduction 29021.2 The Power Divergence (PD) Family 29121.3 Density Power Divergence (DPD) and Parametric Inference 29621.4 A Generalized Form: The S-Divergence 30121.5 Applications 30421.6 Conclusion 306References 30622 COM-Poisson Cure Rate Models and Associated Likelihood-based Inference with Exponential and Weibull Lifetimes 308N. Balakrishnan and Suvra Pal22.1 Introduction 30822.2 Role of Cure Rate Models in Reliability 31022.3 The COM-Poisson Cure Rate Model 31022.4 Data and the Likelihood 31122.5 EM Algorithm 31222.6 Standard Errors and Asymptotic Confidence Intervals 31422.7 Exponential Lifetime Distribution 31422.8 Weibull Lifetime Distribution 32222.9 Analysis of Cutaneous Melanoma Data 33422.10 Conclusion 33722.A1 Appendix A1: E-Step and M-Step Formulas for Exponential Lifetimes 33722.A2 Appendix A2: E-Step and M-Step Formulas for Weibull Lifetimes 34122.B1 Appendix B1: Observed Information Matrix for Exponential Lifetimes 34422.B2 Appendix B2: Observed Information Matrix for Weibull Lifetimes 346References 34723 Exponential Expansions for Perturbed Discrete Time Renewal Equations 349Dmitrii Silvestrov and Mikael Petersson23.1 Introduction 34923.2 Asymptotic Results 35023.3 Proofs 35323.4 Discrete Time Regenerative Processes 35823.5 Queuing and Risk Applications 359References 36124 On Generalized Extreme Shock Models under Renewal Shock Processes 363Ji Hwan Cha and Maxim Finkelstein24.1 Introduction 36324.2 Generalized Extreme Shock Models 36424.3 Specific Models 36724.4 Conclusion 373Acknowledgements 373References 373Part V SYSTEMABILITY, PHYSICS-OF-FAILURE AND RELIABILITY DEMONSTRATION25 Systemability Theory and its Applications 377Hoang Pham25.1 Introduction 37725.2 Systemability Measures 37825.3 Systemability Analysis of k-out-of-n Systems 37925.4 Systemability Function Approximation 38025.5 Systemability with Loglog Distribution 38325.6 Sensitivity Analysis 38425.7 Applications: Red Light Camera Systems 38525.8 Conclusion 387References 38726 Physics-of-Failure based Reliability Engineering 389Pedro O. Quintero and Michael Pecht26.1 Introduction 38926.2 Physics-of-Failure-based Reliability Assessment 39326.3 Uses of Physics-of-Failure 39826.4 Conclusion 400References 40027 Accelerated Testing: Effect of Variance in Field Environmental Conditions on the Demonstrated Reliability 403Andre Kleyner27.1 Introduction 40327.2 Accelerated Testing and Field Stress Variation 40427.3 Case Study: Reliability Demonstration Using Temperature Cycling Test 40527.4 Conclusion 408References 408Index 409