Statistical Reliability Engineering: Methods, Models and Applications (Springer Series in Reliability Engineering)

This book presents the state-of-the-art methodology and detailed analytical models and methods used to assess the reliability of complex systems and related applications in statistical reliability engineering. It is a textbook based mainly on the author’s recent research and publications as well as experience of over 30 years in this field. The book covers a wide range of methods and models in reliability, and their applications, including: statistical methods and model selection for machine learning; models for maintenance and software reliability; statistical reliability estimation of complex systems; and statistical reliability analysis of k out of n systems, standby systems and repairable systems. Offering numerous examples and solved problems within each chapter, this comprehensive text provides an introduction to reliability engineering graduate students, a reference for data scientists and reliability engineers, and a thorough guide for researchers and instructors in the field. Preface Contents About the Author Acronyms 1 Basic Probability, Statistics, and Reliability 1.1 Basic of Probability 1.2 Probability Axioms 1.3 Basic Statistics 1.4 Joint Density Functions of Random LifeTimes 1.5 Conditional Distributions 1.6 Laplace Transformation Functions 1.7 Reliability Concepts 1.7.1 Coherent Systems 1.7.2 Reliability Measures 1.8 Maintainability 1.9 Availability Measure 1.10 Mathematical Techniques 1.11 Probability and Moment Inequalities 1.12 Order Statistics 1.13 Problems Reference 2 Distribution Functions and Its Applications 2.1 Discrete Distributions 2.2 Continuous Distributions 2.3 Characteristics of Failure Rate Functions 2.4 The Central Limit Theorem 2.5 Problems References 3 Statistical Inference 3.1 Introduction 3.2 Statistical Inference 3.3 Parameter Estimation 3.3.1 The Method of Moments 3.3.2 Maximum Likelihood Estimation Method 3.4 Invariance and Lower Bound on the Variance 3.5 Maximum Likelihood Estimation with Censored Data 3.5.1 Parameter Estimate with Multiple-Censored Data 3.5.2 Confidence Intervals of Estimates 3.5.3 Applications 3.6 Statistical Change-Point Estimation Methods 3.6.1 Application: A Software Model with a Change Point 3.7 Goodness of Fit Tests 3.7.1 The Chi-Square Test 3.7.2 Kolmogorov–Smirnov (KS) Test 3.8 Test for Independence 3.9 Statistical Trend Tests of Homogeneous Poisson Process 3.9.1 Laplace Trend Test 3.9.2 Military Handbook Test 3.10 Least Squared Estimation 3.11 Interval Estimation 3.11.1 Confidence Intervals for the Normal Parameters 3.11.2 Confidence Intervals for the Exponential Parameters 3.11.3 Confidence Intervals for the Binomial Parameters 3.11.4 Confidence Intervals for the Poisson Parameters 3.12 Non-Parametric Tolerance Limits 3.13 Sequential Sampling 3.13.1 Exponential Distribution Case 3.14 Bayesian Methods 3.15 Statistical Model Selection 3.15.1 Applications 3.16 Problems References 4 System Reliability Modeling 4.1 Introduction 4.2 Series Systems 4.3 Parallel Systems 4.4 Series–Parallel Systems 4.5 Parallel–Series Systems 4.6 k-out-of-n Systems 4.7 k-to-l-out-of-n Noncoherent Systems 4.8 Standby Systems 4.8.1 Cold Standby Systems with Perfect Switching Device 4.8.2 Cold-Standby Systems with Imperfect Switching Device 4.9 Load-Sharing Systems with Dependent Failures 4.10 Reliability Evaluation of Complex Systems Using Conditional Probability 4.10.1 Applications of Fault-Tolerant Systems Using Decomposition Method 4.11 Degradable Systems 4.12 Dynamic Redundant Systems with Imperfect Coverage 4.13 Noncoherent k-to-l-out-of-n Systems 4.14 Mathematical Optimization 4.15 Reliability of Systems with Multiple Failure Modes 4.15.1 The Series System 4.15.2 The Parallel System 4.15.3 The Parallel–Series System 4.15.4 The Series–Parallel Systems 4.15.5 The k-out-of-n Systems 4.16 Problems 4.17 Projects References 5 System Reliability Estimation 5.1 Order Statistics and Its Application in Reliability 5.2 The k-Out-of-n Systems 5.2.1 k Out of n System Failure Rate 5.3 Reliability Estimation of k-Out-of-n Systems 5.3.1 Failure-Uncensored Case of One-Parameter Exponential Distribution 5.3.2 Failure-Censored Case of One-Parameter Exponential Distribution 5.3.3 Applications 5.3.4 Failure-Uncensored Case of Two-Parameter Exponential Distribution 5.3.5 Applications 5.4 Systemability Measures 5.4.1 Systemability Calculations 5.4.2 Software Reliability Modeling Subject to Random Operating Environments 5.5 Life Testing Cost Model 5.6 Stress-Strength Interval-System Reliability 5.6.1 UMVUE and MLE of Reliability Function 5.6.2 Interval-System Reliability Estimation 5.6.3 Applications 5.7 Problems References 6 Stochastic Processes 6.1 Introduction 6.2 Markov Processes 6.2.1 Three-Non-Identical Unit Load-Sharing Parallel Systems 6.2.2 System Mean Time Between Failures 6.2.3 Degraded Systems 6.2.4 k-Out-Of-n Systems with Degradation 6.2.5 Degraded Systems with Partial Repairs 6.3 Counting Processes 6.3.1 Poisson Processes 6.3.2 Renewal Processes 6.3.3 Quasi-Renewal Processes 6.3.4 Non-homogeneous Poisson Processes 6.4 Problems References 7 Maintenance Models 7.1 Introduction 7.2 Maintenance and Replacement Policies 7.2.1 Age Replacement Policy 7.2.2 Block Replacement 7.2.3 Periodic Replacement Policy 7.2.4 Replacement Models with Two Types of Units 7.3 Non-repairable Degraded System Modeling 7.4 Inspection-Maintenance Repairable Degraded System Modeling 7.5 Warranty Concepts 7.6 Problems References 8 Statistical Machine Learning and Its Applications 8.1 Introduction to Linear Algebra 8.1.1 Definitions and Matrix Calculations 8.2 Singular Value Decomposition 8.2.1 Applications 8.3 Linear Regression Models 8.3.1 Least Squares Estimation 8.3.2 Maximum Likelihood Estimation 8.4 Hypothesis Testing and Confidence Interval Estimation 8.4.1 For Intercept Coefficient 8.4.2 For Slope Coefficient 8.5 Multiple Regression Models 8.5.1 Applications 8.6 Problems Appendix Solutions to Selected Problems Appendix A Distribution Tables Appendix B Laplace Transform Bibliography Index