ELSAYED. A. ELSAYED, PHD is a Distinguished Professor in the Department of Industrial Engineering at Rutgers University. He is Director of the NSF/Industry/University Cooperative Research Center for Quality and Reliability Engineering, Rutgers-Arizona State University. His research interests include the areas of quality and reliability engineering, production planning, and control and manufacturing processes and engineering.

• Preface xiPrelude xvChapter 1 Reliability and Hazard Functions 11.1 Introduction 11.2 Reliability Definition and Estimation 51.3 Hazard Functions 161.4 Multivariate Hazard Rate 571.5 Competing Risk Model and Mixture of Failure Rates 601.6 Discrete Probability Distributions 681.7 Mean Time to Failure 711.8 Mean Residual Life 741.9 Time of First Failure 76Problems 79References 91Chapter 2 System Reliability Evaluation 952.1 Introduction 952.2 Reliability Block Diagrams 962.3 Series Systems 992.4 Parallel Systems 1012.5 Parallel–Series, Series–Parallel, and Mixed-Parallel Systems 1032.6 Consecutive-k-out-of-n:F System 1132.7 Reliability of k-out-of-n Systems 1212.8 Reliability of k-out-of-n Balanced Systems 1232.9 Complex Reliability Systems 1252.10 Special Networks 1432.11 Multistate Models 1442.12 Redundancy 1502.13 Importance Measures of Components 1542.14 Weighted Importance Measures of Components 165Problems 167References 182Chapter 3 Time- and Failure-Dependent Reliability 1853.1 Introduction 1853.2 Nonrepairable Systems 1853.3 Mean Time to Failure 1943.4 Repairable Systems 2043.5 Availability 2153.6 Dependent Failures 2233.7 Redundancy and Standby 228Problems 238References 247Chapter 4 Estimation Methods of the Parameters 2514.1 Introduction 2514.2 Method of Moments 2524.3 The Likelihood Function 2604.4 Method of Least Squares 2784.5 Bayesian Approach 2844.6 Bootstrap Method 2884.7 Generation of Failure Time Data 290Problems 292References 298Chapter 5 Parametric Reliability Models 3015.1 Introduction 3015.2 Approach 1: Historical Data 3025.3 Approach 2: Operational Life Testing 3035.4 Approach 3: Burn-in Testing 3035.5 Approach 4: Accelerated Life Testing 3045.6 Types of Censoring 3055.7 The Exponential Distribution 3085.8 The Rayleigh Distribution 3225.9 The Weibull Distribution 3315.10 The Lognormal Distribution 3435.11 The Gamma Distribution 3505.12 The Extreme Value Distribution 3575.13 The Half-Logistic Distribution 3605.14 The Frechet Distribution 3675.15 The Birnbaum–Saunders Distribution 3695.16 Linear Models 3725.17 Multicensored Data 374Problems 378References 389Chapter 6 Accelerated Life Testing 3936.1 Introduction 3936.2 Types of Reliability Testing 3946.3 Accelerated Life Testing 4036.4 ALT Models 4066.5 Statistics-Based Models: Nonparametric 4206.6 Physics-Statistics-Based Models 4376.7 Physics-Experimental-Based Models 4466.8 Degradation Models 4496.9 Statistical Degradation Models 4536.10 Accelerated Life Testing Plans 459Problems 463References 476Chapter 7 Physics of Failures 4817.1 Introduction 4817.2 Fault Tree Analysis 4817.3 Failure Modes and Effects Analysis 4887.4 Stress–Strength Relationship 4907.5 PoF: Failure Time Models 4927.6 PoF: Degradation Models 512Problems 519References 524Chapter 8 System Resilience 5278.1 Introduction 5278.2 Resilience Overview 5288.3 Multi-Hazard 5288.4 Resilience Modeling 5328.5 Resilience Definitions and Attributes 5358.6 Resilience Quantification 5368.7 Importance Measures 5428.8 Cascading Failures 5448.9 Cyber Networks 546Problems 557References 559Chapter 9 Renewal Processes and Expected Number of Failures 5639.1 Introduction 5639.2 Parametric Renewal Function Estimation 5649.3 Nonparametric Renewal Function Estimation 5789.4 Alternating Renewal Process 5889.5 Approximations of M(t) 5919.6 Other Types of Renewal Processes 5949.7 The Variance of the Number of Renewals 5959.8 Confidence Intervals for the Renewal Function 6019.9 Remaining Life at Time t 6049.10 Poisson Processes 6069.11 Laplace Transform and Random Variables 609Problems 611References 619Chapter 10 Maintenance and Inspection 62110.1 Introduction 62110.2 Preventive Maintenance and Replacement Models: Cost Minimization 62210.3 Preventive Maintenance and Replacement Models: Downtime Minimization 63110.4 Minimal Repair Models 63410.5 Optimum Replacement Intervals for Systems Subject to Shocks 63910.6 Preventive Maintenance and Number of Spares 64210.7 Group Maintenance 64910.8 Periodic Inspection 65310.9 Condition-Based Maintenance 66310.10 On-Line Surveillance and Monitoring 665Problems 669References 676Chapter 11 Warranty Models 67911.1 Introduction 67911.2 Warranty Models for Nonrepairable Products 68111.3 Warranty Models for Repairable Products 70111.4 Two-Dimensional Warranty 71611.5 Warranty Claims 718Problems 725References 731Chapter 12 Case Studies 73312.1 Case 1: A Crane Spreader Subsystem 73312.2 Case 2: Design of a Production Line 73912.3 Case 3: An Explosive Detection System 74612.4 Case 4: Reliability of Furnace Tubes 75212.5 Case 5: Reliability of Smart Cards 75712.6 Case 6: Life Distribution of Survivors of Qualification and Certification 76012.7 Case 7: Reliability Modeling of Telecommunication Networks for the Air Traffic Control System 76712.8 Case 8: System Design Using Reliability Objectives 77612.9 Case 9: Reliability Modeling of Hydraulic Fracture Pumps 78612.10 Case 10: Availability of Medical Information Technology System 79112.11 Case 11: Producer and Consumer Risk in System of Systems 797References 804AppendicesAppendix A Gamma Table 805Appendix B Computer Program To Calculate the Reliability of a Consecutive-k-Out-of-n:F System 811Appendix C Optimum Arrangement of Components In Consecutive-2-Out-of-N:F Systems 813Appendix D Computer Program For Solving the Time-Dependent Equations 821Appendix E The Newton–Raphson Method 823Appendix F Coefficients of bi’s For i = 1, …, n 829Appendix G Variance of θ∗2’s In Terms of θ22/n and K3/K∗2 843Appendix H Computer Listing of the Newton–Raphson Method 849Appendix I Coefficients (ai and bi) of the Best Estimates of the Mean (μ) and Standard Deviation (σ) In Censored Samples Up To n = 20 From a Normal Population 851Appendix J Baker’s Algorithm 865Appendix K Standard Normal Distribution 869Appendix L Critical Values of χ2 875Appendix M Solutions of Selected Problems 879Author Index 887Subject Index 895

ELSAYED. A. ELSAYED, PHD is a Distinguished Professor in the Department of Industrial Engineering at Rutgers University. He is Director of the NSF/Industry/University Cooperative Research Center for Quality and Reliability Engineering, Rutgers-Arizona State University. His research interests include the areas of quality and reliability engineering, production planning, and control and manufacturing processes and engineering.

• Preface xiPrelude xvChapter 1 Reliability and Hazard Functions 11.1 Introduction 11.2 Reliability Definition and Estimation 51.3 Hazard Functions 161.4 Multivariate Hazard Rate 571.5 Competing Risk Model and Mixture of Failure Rates 601.6 Discrete Probability Distributions 681.7 Mean Time to Failure 711.8 Mean Residual Life 741.9 Time of First Failure 76Problems 79References 91Chapter 2 System Reliability Evaluation 952.1 Introduction 952.2 Reliability Block Diagrams 962.3 Series Systems 992.4 Parallel Systems 1012.5 Parallel–Series, Series–Parallel, and Mixed-Parallel Systems 1032.6 Consecutive-k-out-of-n:F System 1132.7 Reliability of k-out-of-n Systems 1212.8 Reliability of k-out-of-n Balanced Systems 1232.9 Complex Reliability Systems 1252.10 Special Networks 1432.11 Multistate Models 1442.12 Redundancy 1502.13 Importance Measures of Components 1542.14 Weighted Importance Measures of Components 165Problems 167References 182Chapter 3 Time- and Failure-Dependent Reliability 1853.1 Introduction 1853.2 Nonrepairable Systems 1853.3 Mean Time to Failure 1943.4 Repairable Systems 2043.5 Availability 2153.6 Dependent Failures 2233.7 Redundancy and Standby 228Problems 238References 247Chapter 4 Estimation Methods of the Parameters 2514.1 Introduction 2514.2 Method of Moments 2524.3 The Likelihood Function 2604.4 Method of Least Squares 2784.5 Bayesian Approach 2844.6 Bootstrap Method 2884.7 Generation of Failure Time Data 290Problems 292References 298Chapter 5 Parametric Reliability Models 3015.1 Introduction 3015.2 Approach 1: Historical Data 3025.3 Approach 2: Operational Life Testing 3035.4 Approach 3: Burn-in Testing 3035.5 Approach 4: Accelerated Life Testing 3045.6 Types of Censoring 3055.7 The Exponential Distribution 3085.8 The Rayleigh Distribution 3225.9 The Weibull Distribution 3315.10 The Lognormal Distribution 3435.11 The Gamma Distribution 3505.12 The Extreme Value Distribution 3575.13 The Half-Logistic Distribution 3605.14 The Frechet Distribution 3675.15 The Birnbaum–Saunders Distribution 3695.16 Linear Models 3725.17 Multicensored Data 374Problems 378References 389Chapter 6 Accelerated Life Testing 3936.1 Introduction 3936.2 Types of Reliability Testing 3946.3 Accelerated Life Testing 4036.4 ALT Models 4066.5 Statistics-Based Models: Nonparametric 4206.6 Physics-Statistics-Based Models 4376.7 Physics-Experimental-Based Models 4466.8 Degradation Models 4496.9 Statistical Degradation Models 4536.10 Accelerated Life Testing Plans 459Problems 463References 476Chapter 7 Physics of Failures 4817.1 Introduction 4817.2 Fault Tree Analysis 4817.3 Failure Modes and Effects Analysis 4887.4 Stress–Strength Relationship 4907.5 PoF: Failure Time Models 4927.6 PoF: Degradation Models 512Problems 519References 524Chapter 8 System Resilience 5278.1 Introduction 5278.2 Resilience Overview 5288.3 Multi-Hazard 5288.4 Resilience Modeling 5328.5 Resilience Definitions and Attributes 5358.6 Resilience Quantification 5368.7 Importance Measures 5428.8 Cascading Failures 5448.9 Cyber Networks 546Problems 557References 559Chapter 9 Renewal Processes and Expected Number of Failures 5639.1 Introduction 5639.2 Parametric Renewal Function Estimation 5649.3 Nonparametric Renewal Function Estimation 5789.4 Alternating Renewal Process 5889.5 Approximations of M(t) 5919.6 Other Types of Renewal Processes 5949.7 The Variance of the Number of Renewals 5959.8 Confidence Intervals for the Renewal Function 6019.9 Remaining Life at Time t 6049.10 Poisson Processes 6069.11 Laplace Transform and Random Variables 609Problems 611References 619Chapter 10 Maintenance and Inspection 62110.1 Introduction 62110.2 Preventive Maintenance and Replacement Models: Cost Minimization 62210.3 Preventive Maintenance and Replacement Models: Downtime Minimization 63110.4 Minimal Repair Models 63410.5 Optimum Replacement Intervals for Systems Subject to Shocks 63910.6 Preventive Maintenance and Number of Spares 64210.7 Group Maintenance 64910.8 Periodic Inspection 65310.9 Condition-Based Maintenance 66310.10 On-Line Surveillance and Monitoring 665Problems 669References 676Chapter 11 Warranty Models 67911.1 Introduction 67911.2 Warranty Models for Nonrepairable Products 68111.3 Warranty Models for Repairable Products 70111.4 Two-Dimensional Warranty 71611.5 Warranty Claims 718Problems 725References 731Chapter 12 Case Studies 73312.1 Case 1: A Crane Spreader Subsystem 73312.2 Case 2: Design of a Production Line 73912.3 Case 3: An Explosive Detection System 74612.4 Case 4: Reliability of Furnace Tubes 75212.5 Case 5: Reliability of Smart Cards 75712.6 Case 6: Life Distribution of Survivors of Qualification and Certification 76012.7 Case 7: Reliability Modeling of Telecommunication Networks for the Air Traffic Control System 76712.8 Case 8: System Design Using Reliability Objectives 77612.9 Case 9: Reliability Modeling of Hydraulic Fracture Pumps 78612.10 Case 10: Availability of Medical Information Technology System 79112.11 Case 11: Producer and Consumer Risk in System of Systems 797References 804AppendicesAppendix A Gamma Table 805Appendix B Computer Program To Calculate the Reliability of a Consecutive-k-Out-of-n:F System 811Appendix C Optimum Arrangement of Components In Consecutive-2-Out-of-N:F Systems 813Appendix D Computer Program For Solving the Time-Dependent Equations 821Appendix E The Newton–Raphson Method 823Appendix F Coefficients of bi’s For i = 1, …, n 829Appendix G Variance of θ∗2’s In Terms of θ22/n and K3/K∗2 843Appendix H Computer Listing of the Newton–Raphson Method 849Appendix I Coefficients (ai and bi) of the Best Estimates of the Mean (μ) and Standard Deviation (σ) In Censored Samples Up To n = 20 From a Normal Population 851Appendix J Baker’s Algorithm 865Appendix K Standard Normal Distribution 869Appendix L Critical Values of χ2 875Appendix M Solutions of Selected Problems 879Author Index 887Subject Index 895

ELSAYED. A. ELSAYED, PHD is a Distinguished Professor in the Department of Industrial Engineering at Rutgers University. He is Director of the NSF/Industry/University Cooperative Research Center for Quality and Reliability Engineering, Rutgers-Arizona State University. His research interests include the areas of quality and reliability engineering, production planning, and control and manufacturing processes and engineering.

• Preface xiPrelude xvChapter 1 Reliability and Hazard Functions 11.1 Introduction 11.2 Reliability Definition and Estimation 51.3 Hazard Functions 161.4 Multivariate Hazard Rate 571.5 Competing Risk Model and Mixture of Failure Rates 601.6 Discrete Probability Distributions 681.7 Mean Time to Failure 711.8 Mean Residual Life 741.9 Time of First Failure 76Problems 79References 91Chapter 2 System Reliability Evaluation 952.1 Introduction 952.2 Reliability Block Diagrams 962.3 Series Systems 992.4 Parallel Systems 1012.5 Parallel–Series, Series–Parallel, and Mixed-Parallel Systems 1032.6 Consecutive-k-out-of-n:F System 1132.7 Reliability of k-out-of-n Systems 1212.8 Reliability of k-out-of-n Balanced Systems 1232.9 Complex Reliability Systems 1252.10 Special Networks 1432.11 Multistate Models 1442.12 Redundancy 1502.13 Importance Measures of Components 1542.14 Weighted Importance Measures of Components 165Problems 167References 182Chapter 3 Time- and Failure-Dependent Reliability 1853.1 Introduction 1853.2 Nonrepairable Systems 1853.3 Mean Time to Failure 1943.4 Repairable Systems 2043.5 Availability 2153.6 Dependent Failures 2233.7 Redundancy and Standby 228Problems 238References 247Chapter 4 Estimation Methods of the Parameters 2514.1 Introduction 2514.2 Method of Moments 2524.3 The Likelihood Function 2604.4 Method of Least Squares 2784.5 Bayesian Approach 2844.6 Bootstrap Method 2884.7 Generation of Failure Time Data 290Problems 292References 298Chapter 5 Parametric Reliability Models 3015.1 Introduction 3015.2 Approach 1: Historical Data 3025.3 Approach 2: Operational Life Testing 3035.4 Approach 3: Burn-in Testing 3035.5 Approach 4: Accelerated Life Testing 3045.6 Types of Censoring 3055.7 The Exponential Distribution 3085.8 The Rayleigh Distribution 3225.9 The Weibull Distribution 3315.10 The Lognormal Distribution 3435.11 The Gamma Distribution 3505.12 The Extreme Value Distribution 3575.13 The Half-Logistic Distribution 3605.14 The Frechet Distribution 3675.15 The Birnbaum–Saunders Distribution 3695.16 Linear Models 3725.17 Multicensored Data 374Problems 378References 389Chapter 6 Accelerated Life Testing 3936.1 Introduction 3936.2 Types of Reliability Testing 3946.3 Accelerated Life Testing 4036.4 ALT Models 4066.5 Statistics-Based Models: Nonparametric 4206.6 Physics-Statistics-Based Models 4376.7 Physics-Experimental-Based Models 4466.8 Degradation Models 4496.9 Statistical Degradation Models 4536.10 Accelerated Life Testing Plans 459Problems 463References 476Chapter 7 Physics of Failures 4817.1 Introduction 4817.2 Fault Tree Analysis 4817.3 Failure Modes and Effects Analysis 4887.4 Stress–Strength Relationship 4907.5 PoF: Failure Time Models 4927.6 PoF: Degradation Models 512Problems 519References 524Chapter 8 System Resilience 5278.1 Introduction 5278.2 Resilience Overview 5288.3 Multi-Hazard 5288.4 Resilience Modeling 5328.5 Resilience Definitions and Attributes 5358.6 Resilience Quantification 5368.7 Importance Measures 5428.8 Cascading Failures 5448.9 Cyber Networks 546Problems 557References 559Chapter 9 Renewal Processes and Expected Number of Failures 5639.1 Introduction 5639.2 Parametric Renewal Function Estimation 5649.3 Nonparametric Renewal Function Estimation 5789.4 Alternating Renewal Process 5889.5 Approximations of M(t) 5919.6 Other Types of Renewal Processes 5949.7 The Variance of the Number of Renewals 5959.8 Confidence Intervals for the Renewal Function 6019.9 Remaining Life at Time t 6049.10 Poisson Processes 6069.11 Laplace Transform and Random Variables 609Problems 611References 619Chapter 10 Maintenance and Inspection 62110.1 Introduction 62110.2 Preventive Maintenance and Replacement Models: Cost Minimization 62210.3 Preventive Maintenance and Replacement Models: Downtime Minimization 63110.4 Minimal Repair Models 63410.5 Optimum Replacement Intervals for Systems Subject to Shocks 63910.6 Preventive Maintenance and Number of Spares 64210.7 Group Maintenance 64910.8 Periodic Inspection 65310.9 Condition-Based Maintenance 66310.10 On-Line Surveillance and Monitoring 665Problems 669References 676Chapter 11 Warranty Models 67911.1 Introduction 67911.2 Warranty Models for Nonrepairable Products 68111.3 Warranty Models for Repairable Products 70111.4 Two-Dimensional Warranty 71611.5 Warranty Claims 718Problems 725References 731Chapter 12 Case Studies 73312.1 Case 1: A Crane Spreader Subsystem 73312.2 Case 2: Design of a Production Line 73912.3 Case 3: An Explosive Detection System 74612.4 Case 4: Reliability of Furnace Tubes 75212.5 Case 5: Reliability of Smart Cards 75712.6 Case 6: Life Distribution of Survivors of Qualification and Certification 76012.7 Case 7: Reliability Modeling of Telecommunication Networks for the Air Traffic Control System 76712.8 Case 8: System Design Using Reliability Objectives 77612.9 Case 9: Reliability Modeling of Hydraulic Fracture Pumps 78612.10 Case 10: Availability of Medical Information Technology System 79112.11 Case 11: Producer and Consumer Risk in System of Systems 797References 804AppendicesAppendix A Gamma Table 805Appendix B Computer Program To Calculate the Reliability of a Consecutive-k-Out-of-n:F System 811Appendix C Optimum Arrangement of Components In Consecutive-2-Out-of-N:F Systems 813Appendix D Computer Program For Solving the Time-Dependent Equations 821Appendix E The Newton–Raphson Method 823Appendix F Coefficients of bi’s For i = 1, …, n 829Appendix G Variance of θ∗2’s In Terms of θ22/n and K3/K∗2 843Appendix H Computer Listing of the Newton–Raphson Method 849Appendix I Coefficients (ai and bi) of the Best Estimates of the Mean (μ) and Standard Deviation (σ) In Censored Samples Up To n = 20 From a Normal Population 851Appendix J Baker’s Algorithm 865Appendix K Standard Normal Distribution 869Appendix L Critical Values of χ2 875Appendix M Solutions of Selected Problems 879Author Index 887Subject Index 895