Contents:

Summary: 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.
Cover -- Title Page -- Copyright -- Contents -- Remembering Boris Gnedenko -- List of Contributors -- Preface -- Acknowledgements -- Part I Degradation Analysis, Multi-State and Continuous-State System Reliability -- Chapter 1 Methods of Solutions of Inhomogeneous Continuous Time Markov Chains for Degradation Process Modeling -- 1.1 Introduction -- 1.2 Formalism of ICTMC -- 1.3 Numerical Solution Techniques -- 1.3.1 The Runge-Kutta Method -- 1.3.2 Uniformization -- 1.3.3 Monte Carlo Simulation -- 1.3.4 State-Space Enrichment -- 1.4 Examples -- 1.4.1 Example of Computing System Degradation -- 1.4.2 Example of Nuclear Component Degradation -- 1.5 Comparisons of the Methods and Guidelines of Utilization -- 1.6 Conclusion -- References -- Chapter 2 Multistate Degradation and Condition Monitoring for Devices with Multiple Independent Failure Modes -- 2.1 Introduction -- 2.2 Multistate Degradation and Multiple Independent Failure Modes -- 2.2.1 Notation -- 2.2.2 Assumptions -- 2.2.3 The Stochastic Process Model -- 2.3 Parameter Estimation -- 2.4 Important Reliability Measures of a Condition-Monitored Device -- 2.5 Numerical Example -- 2.6 Conclusion -- Acknowledgements -- References -- Chapter 3 Time Series Regression with Exponential Errors for Accelerated Testing and Degradation Tracking -- 3.1 Introduction -- 3.2 Preliminaries: Statement of the Problem -- 3.2.1 Relevance to Accelerated Testing, Degradation and Risk -- 3.3 Estimation and Prediction by Least Squares -- 3.4 Estimation and Prediction by MLE -- 3.4.1 Properties of the Maximum Likelihood Estimator -- 3.5 The Bayesian Approach: The Predictive Distribution -- 3.5.1 The Predictive Distribution of YT+1 when λ > A -- 3.5.2 The Predictive Distribution of YT+1 when λ ≤ A -- 3.5.3 Alternative Prior for β -- Acknowledgements -- References.

Chapter 4 Inverse Lz-Transform for a Discrete-State Continuous-Time Markov Process and Its Application to Multi-State System Reliability Analysis -- 4.1 Introduction -- 4.2 Inverse Lz-Transform: Definitions and Computational Procedure -- 4.2.1 Definitions -- 4.2.2 Computational Procedure -- 4.3 Application of Inverse Lz-Transform to MSS Reliability Analysis -- 4.4 Numerical Example -- 4.5 Conclusion -- References -- Chapter 5 On the Lz-Transform Application for Availability Assessment of an Aging Multi-State Water Cooling System for Medical Equipment -- 5.1 Introduction -- 5.2 Brief Description of the Lz-Transform Method -- 5.3 Multi-state Model of the Water Cooling System for the MRI Equipment -- 5.3.1 System Description -- 5.3.2 The Chiller Sub-System -- 5.3.3 The Heat Exchanger Sub-System -- 5.3.4 The Pump Sub-System -- 5.3.5 The Electric Board Sub-System -- 5.3.6 Model of Stochastic Demand -- 5.3.7 Multi-State Model for the MRI Cooling System -- 5.4 Availability Calculation -- 5.5 Conclusion -- Acknowledgments -- References -- Chapter 6 Combined Clustering and Lz-Transform Technique to Reduce the Computational Complexity of a Multi-State System Reliability Evaluation -- 6.1 Introduction -- 6.2 The Lz-Transform for Dynamic Reliability Evaluation for MSS -- 6.3 Clustering Composition Operator in the Lz-Transform -- 6.4 Computational Procedures -- 6.5 Numerical Example -- 6.6 Conclusion -- References -- Chapter 7 Sliding Window Systems with Gaps -- 7.1 Introduction -- 7.2 The Models -- 7.2.1 The k/eSWS Model -- 7.2.2 The mCSWS Model -- 7.2.3 The mGSWS Model -- 7.2.4 Interrelations among Different Models -- 7.3 Reliability Evaluation Technique -- 7.3.1 Determining u-functions for Individual Elements and their Groups -- 7.3.2 Determining u-functions for all the Groups of r Consecutive Elements -- 7.3.3 Detecting the System Failure.

7.3.4 Updating the Counter -- 7.3.5 Recursive Determination of System Failure Probability -- 7.3.6 Computational Complexity Reduction -- 7.3.7 Algorithm for System Reliability Evaluation -- 7.4 Conclusion -- References -- Chapter 8 Development of Reliability Measures Motivated by Fuzzy Sets for Systems with Multi- or Infinite-States -- 8.1 Introduction -- 8.2 Models for Components and Systems Using Fuzzy Sets -- 8.2.1 Binary Reliability and Multi-State Reliability Model -- 8.2.2 Definition of Fuzzy Reliability -- 8.2.3 Fuzzy Unreliability: A Different Perspective -- 8.2.4 Evolution from Binary State to Multi-State and to Fuzzy State Reliability Modeling -- 8.3 Fuzzy Reliability for Systems with Continuous or Infinite States -- 8.4 Dynamic Fuzzy Reliability -- 8.4.1 Time to Fuzzy Failure Modeled by Fuzzy Random Variable -- 8.4.2 Stochastic Performance Degradation Model -- 8.4.3 Membership Function Evaluation for the Expectation of Time to Fuzzy Failure -- 8.4.4 Performance Measures for Dynamic Fuzzy Reliability -- 8.5 System Fuzzy Reliability -- 8.6 Examples and Applications -- 8.6.1 Reliability Performance Evaluation Based on Time to Fuzzy Failure -- 8.6.2 Example for System Fuzzy Reliability Modeling -- 8.6.3 Numerical Results -- 8.7 Conclusion -- References -- Chapter 9 Imperatives for Performability Design in the Twenty-First Century -- 9.1 Introduction -- 9.2 Strategies for Sustainable Development -- 9.2.1 The Internalization of Hidden Costs -- 9.2.2 Mitigation Policies -- 9.2.3 Dematerialization -- 9.2.4 Minimization of Energy Requirement -- 9.3 Reappraisal of the Performance of Products and Systems -- 9.4 Dependability and Environmental Risk are Interdependent -- 9.5 Performability: An Appropriate Measure of Performance -- 9.5.1 Performability Engineering -- 9.6 Towards Dependable and Sustainable Designs -- 9.7 Conclusion -- References.

Part II Networks and Large-Scale Systems -- Chapter 10 Network Reliability Calculations Based on Structural Invariants -- 10.1 First Invariant: D-Spectrum, Signature -- 10.2 Second Invariant: Importance Spectrum. Birnbaum Importance Measure (BIM) -- 10.3 Example: Reliability of a Road Network -- 10.4 Third Invariant: Border States -- 10.5 Monte Carlo to Approximate the Invariants -- 10.6 Conclusion -- References -- Chapter 11 Performance and Availability Evaluation of IMS-Based Core Networks -- 11.1 Introduction -- 11.2 IMS-Based Core Network Description -- 11.3 Analytic Models for Independent Software Recovery -- 11.3.1 Model 1: Hierarchical Model with Top-Level RBD and Lower-Level MFT -- 11.3.2 Model 2: Hierarchical Model with Top-Level RBD and Lower-Level FT -- 11.3.3 Model 3: Hierarchical Model with Top-Level RBD and Lower-Level SRN -- 11.4 Analytic Models for Recovery with Dependencies -- 11.4.1 Model 4: Hierarchical Model with Top-Level RBD, Middle-Level MFT and Lower-Level CTMC -- 11.4.2 Model 5: Alternative Approach for Model 4 based on UGF -- 11.4.3 Model 6: Hierarchical Model with Top-Level RBD and Lower-Level SRN -- 11.5 Redundancy Optimization -- 11.6 Numerical Results -- 11.6.1 Model Comparison -- 11.6.2 Influences of Performance Demand and Redundancy Configuration -- 11.7 Conclusion -- References -- Chapter 12 Reliability and Probability of First Occurred Failure for Discrete-Time Semi-Markov Systems -- 12.1 Introduction -- 12.2 Discrete-Time Semi-Markov Model -- 12.3 Reliability and Probability of First Occurred Failure -- 12.3.1 Rate of Occurrence of Failures -- 12.3.2 Steady-State Availability -- 12.3.3 Probability of First Occurred Failure -- 12.4 Nonparametric Estimation of Reliability Measures -- 12.4.1 Estimation of ROCOF -- 12.4.2 Estimation of the Steady-State Availability.

12.4.3 Estimation of the Probability of First Occurred Failure -- 12.5 Numerical Application -- 12.6 Conclusion -- References -- Chapter 13 Single-Source Epidemic Process in a System of Two Interconnected Networks -- 13.1 Introduction -- 13.2 Failure Process and the Distribution of the Number of Failed Nodes -- 13.3 Network Failure Probabilities -- 13.4 Example -- 13.5 Conclusion -- Appendix D: Spectrum (Signature) -- References -- Part III Maintenance Models -- Chapter 14 Comparisons of Periodic and Random Replacement Policies -- 14.1 Introduction -- 14.2 Four Policies -- 14.2.1 Standard Replacement -- 14.2.2 Replacement First -- 14.2.3 Replacement Last -- 14.2.4 Replacement Over Time -- 14.3 Comparisons of Optimal Policies -- 14.3.1 Comparisons of T S* and T F*, T L*, and T O* -- 14.3.2 Comparisons of T O* and T F*, T L* -- 14.3.3 Comparisons of T F* and T L* -- 14.4 Numerical Examples 1 -- 14.5 Comparisons of Policies with Different Replacement Costs -- 14.5.1 Comparisons of T S*, and T F*, T L* -- 14.5.2 Comparisons of T S* and T O* -- 14.6 Numerical Examples 2 -- 14.7 Conclusion -- Acknowledgements -- References -- Chapter 15 Random Evolution of Degradation and Occurrences of Words in Random Sequences of Letters -- 15.1 Introduction -- 15.2 Waiting Times to Words' Occurrences -- 15.2.1 The Markov Chain Approach -- 15.2.2 Leading Numbers and Occurrences Times -- 15.3 Some Reliability-Maintenance Models -- 15.3.1 Model 1 (Simple Machine Replacement) -- 15.3.2 Model 2 (Random Reduction of Age) -- 15.3.3 Model 3 (Random Number of Effective Repairs in a Parallel System) -- 15.3.4 Degradation and Words -- 15.4 Waiting Times to Occurrences of Words and Stochastic Comparisons for Degradation -- 15.5 Conclusions -- Acknowledgements -- References -- Chapter 16 Occupancy Times for Markov and Semi-Markov Models in Systems Reliability -- 16.1 Introduction.

16.2 Markov Models for Systems Reliability.

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Cover -- Title Page -- Copyright -- Contents -- Remembering Boris Gnedenko -- List of Contributors -- Preface -- Acknowledgements -- Part I Degradation Analysis, Multi-State and Continuous-State System Reliability -- Chapter 1 Methods of Solutions of Inhomogeneous Continuous Time Markov Chains for Degradation Process Modeling -- 1.1 Introduction -- 1.2 Formalism of ICTMC -- 1.3 Numerical Solution Techniques -- 1.3.1 The Runge-Kutta Method -- 1.3.2 Uniformization -- 1.3.3 Monte Carlo Simulation -- 1.3.4 State-Space Enrichment -- 1.4 Examples -- 1.4.1 Example of Computing System Degradation -- 1.4.2 Example of Nuclear Component Degradation -- 1.5 Comparisons of the Methods and Guidelines of Utilization -- 1.6 Conclusion -- References -- Chapter 2 Multistate Degradation and Condition Monitoring for Devices with Multiple Independent Failure Modes -- 2.1 Introduction -- 2.2 Multistate Degradation and Multiple Independent Failure Modes -- 2.2.1 Notation -- 2.2.2 Assumptions -- 2.2.3 The Stochastic Process Model -- 2.3 Parameter Estimation -- 2.4 Important Reliability Measures of a Condition-Monitored Device -- 2.5 Numerical Example -- 2.6 Conclusion -- Acknowledgements -- References -- Chapter 3 Time Series Regression with Exponential Errors for Accelerated Testing and Degradation Tracking -- 3.1 Introduction -- 3.2 Preliminaries: Statement of the Problem -- 3.2.1 Relevance to Accelerated Testing, Degradation and Risk -- 3.3 Estimation and Prediction by Least Squares -- 3.4 Estimation and Prediction by MLE -- 3.4.1 Properties of the Maximum Likelihood Estimator -- 3.5 The Bayesian Approach: The Predictive Distribution -- 3.5.1 The Predictive Distribution of YT+1 when λ > A -- 3.5.2 The Predictive Distribution of YT+1 when λ ≤ A -- 3.5.3 Alternative Prior for β -- Acknowledgements -- References.

Chapter 4 Inverse Lz-Transform for a Discrete-State Continuous-Time Markov Process and Its Application to Multi-State System Reliability Analysis -- 4.1 Introduction -- 4.2 Inverse Lz-Transform: Definitions and Computational Procedure -- 4.2.1 Definitions -- 4.2.2 Computational Procedure -- 4.3 Application of Inverse Lz-Transform to MSS Reliability Analysis -- 4.4 Numerical Example -- 4.5 Conclusion -- References -- Chapter 5 On the Lz-Transform Application for Availability Assessment of an Aging Multi-State Water Cooling System for Medical Equipment -- 5.1 Introduction -- 5.2 Brief Description of the Lz-Transform Method -- 5.3 Multi-state Model of the Water Cooling System for the MRI Equipment -- 5.3.1 System Description -- 5.3.2 The Chiller Sub-System -- 5.3.3 The Heat Exchanger Sub-System -- 5.3.4 The Pump Sub-System -- 5.3.5 The Electric Board Sub-System -- 5.3.6 Model of Stochastic Demand -- 5.3.7 Multi-State Model for the MRI Cooling System -- 5.4 Availability Calculation -- 5.5 Conclusion -- Acknowledgments -- References -- Chapter 6 Combined Clustering and Lz-Transform Technique to Reduce the Computational Complexity of a Multi-State System Reliability Evaluation -- 6.1 Introduction -- 6.2 The Lz-Transform for Dynamic Reliability Evaluation for MSS -- 6.3 Clustering Composition Operator in the Lz-Transform -- 6.4 Computational Procedures -- 6.5 Numerical Example -- 6.6 Conclusion -- References -- Chapter 7 Sliding Window Systems with Gaps -- 7.1 Introduction -- 7.2 The Models -- 7.2.1 The k/eSWS Model -- 7.2.2 The mCSWS Model -- 7.2.3 The mGSWS Model -- 7.2.4 Interrelations among Different Models -- 7.3 Reliability Evaluation Technique -- 7.3.1 Determining u-functions for Individual Elements and their Groups -- 7.3.2 Determining u-functions for all the Groups of r Consecutive Elements -- 7.3.3 Detecting the System Failure.

7.3.4 Updating the Counter -- 7.3.5 Recursive Determination of System Failure Probability -- 7.3.6 Computational Complexity Reduction -- 7.3.7 Algorithm for System Reliability Evaluation -- 7.4 Conclusion -- References -- Chapter 8 Development of Reliability Measures Motivated by Fuzzy Sets for Systems with Multi- or Infinite-States -- 8.1 Introduction -- 8.2 Models for Components and Systems Using Fuzzy Sets -- 8.2.1 Binary Reliability and Multi-State Reliability Model -- 8.2.2 Definition of Fuzzy Reliability -- 8.2.3 Fuzzy Unreliability: A Different Perspective -- 8.2.4 Evolution from Binary State to Multi-State and to Fuzzy State Reliability Modeling -- 8.3 Fuzzy Reliability for Systems with Continuous or Infinite States -- 8.4 Dynamic Fuzzy Reliability -- 8.4.1 Time to Fuzzy Failure Modeled by Fuzzy Random Variable -- 8.4.2 Stochastic Performance Degradation Model -- 8.4.3 Membership Function Evaluation for the Expectation of Time to Fuzzy Failure -- 8.4.4 Performance Measures for Dynamic Fuzzy Reliability -- 8.5 System Fuzzy Reliability -- 8.6 Examples and Applications -- 8.6.1 Reliability Performance Evaluation Based on Time to Fuzzy Failure -- 8.6.2 Example for System Fuzzy Reliability Modeling -- 8.6.3 Numerical Results -- 8.7 Conclusion -- References -- Chapter 9 Imperatives for Performability Design in the Twenty-First Century -- 9.1 Introduction -- 9.2 Strategies for Sustainable Development -- 9.2.1 The Internalization of Hidden Costs -- 9.2.2 Mitigation Policies -- 9.2.3 Dematerialization -- 9.2.4 Minimization of Energy Requirement -- 9.3 Reappraisal of the Performance of Products and Systems -- 9.4 Dependability and Environmental Risk are Interdependent -- 9.5 Performability: An Appropriate Measure of Performance -- 9.5.1 Performability Engineering -- 9.6 Towards Dependable and Sustainable Designs -- 9.7 Conclusion -- References.

Part II Networks and Large-Scale Systems -- Chapter 10 Network Reliability Calculations Based on Structural Invariants -- 10.1 First Invariant: D-Spectrum, Signature -- 10.2 Second Invariant: Importance Spectrum. Birnbaum Importance Measure (BIM) -- 10.3 Example: Reliability of a Road Network -- 10.4 Third Invariant: Border States -- 10.5 Monte Carlo to Approximate the Invariants -- 10.6 Conclusion -- References -- Chapter 11 Performance and Availability Evaluation of IMS-Based Core Networks -- 11.1 Introduction -- 11.2 IMS-Based Core Network Description -- 11.3 Analytic Models for Independent Software Recovery -- 11.3.1 Model 1: Hierarchical Model with Top-Level RBD and Lower-Level MFT -- 11.3.2 Model 2: Hierarchical Model with Top-Level RBD and Lower-Level FT -- 11.3.3 Model 3: Hierarchical Model with Top-Level RBD and Lower-Level SRN -- 11.4 Analytic Models for Recovery with Dependencies -- 11.4.1 Model 4: Hierarchical Model with Top-Level RBD, Middle-Level MFT and Lower-Level CTMC -- 11.4.2 Model 5: Alternative Approach for Model 4 based on UGF -- 11.4.3 Model 6: Hierarchical Model with Top-Level RBD and Lower-Level SRN -- 11.5 Redundancy Optimization -- 11.6 Numerical Results -- 11.6.1 Model Comparison -- 11.6.2 Influences of Performance Demand and Redundancy Configuration -- 11.7 Conclusion -- References -- Chapter 12 Reliability and Probability of First Occurred Failure for Discrete-Time Semi-Markov Systems -- 12.1 Introduction -- 12.2 Discrete-Time Semi-Markov Model -- 12.3 Reliability and Probability of First Occurred Failure -- 12.3.1 Rate of Occurrence of Failures -- 12.3.2 Steady-State Availability -- 12.3.3 Probability of First Occurred Failure -- 12.4 Nonparametric Estimation of Reliability Measures -- 12.4.1 Estimation of ROCOF -- 12.4.2 Estimation of the Steady-State Availability.

12.4.3 Estimation of the Probability of First Occurred Failure -- 12.5 Numerical Application -- 12.6 Conclusion -- References -- Chapter 13 Single-Source Epidemic Process in a System of Two Interconnected Networks -- 13.1 Introduction -- 13.2 Failure Process and the Distribution of the Number of Failed Nodes -- 13.3 Network Failure Probabilities -- 13.4 Example -- 13.5 Conclusion -- Appendix D: Spectrum (Signature) -- References -- Part III Maintenance Models -- Chapter 14 Comparisons of Periodic and Random Replacement Policies -- 14.1 Introduction -- 14.2 Four Policies -- 14.2.1 Standard Replacement -- 14.2.2 Replacement First -- 14.2.3 Replacement Last -- 14.2.4 Replacement Over Time -- 14.3 Comparisons of Optimal Policies -- 14.3.1 Comparisons of T S* and T F*, T L*, and T O* -- 14.3.2 Comparisons of T O* and T F*, T L* -- 14.3.3 Comparisons of T F* and T L* -- 14.4 Numerical Examples 1 -- 14.5 Comparisons of Policies with Different Replacement Costs -- 14.5.1 Comparisons of T S*, and T F*, T L* -- 14.5.2 Comparisons of T S* and T O* -- 14.6 Numerical Examples 2 -- 14.7 Conclusion -- Acknowledgements -- References -- Chapter 15 Random Evolution of Degradation and Occurrences of Words in Random Sequences of Letters -- 15.1 Introduction -- 15.2 Waiting Times to Words' Occurrences -- 15.2.1 The Markov Chain Approach -- 15.2.2 Leading Numbers and Occurrences Times -- 15.3 Some Reliability-Maintenance Models -- 15.3.1 Model 1 (Simple Machine Replacement) -- 15.3.2 Model 2 (Random Reduction of Age) -- 15.3.3 Model 3 (Random Number of Effective Repairs in a Parallel System) -- 15.3.4 Degradation and Words -- 15.4 Waiting Times to Occurrences of Words and Stochastic Comparisons for Degradation -- 15.5 Conclusions -- Acknowledgements -- References -- Chapter 16 Occupancy Times for Markov and Semi-Markov Models in Systems Reliability -- 16.1 Introduction.

16.2 Markov Models for Systems Reliability.

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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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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