Reliability Engineering (3^rd Ed.)
Wiley Series in Systems Engineering and Management Series

• Reliability and hazard functions, like the Weibull Model, the Exponential Model, the Gamma Model, and the Log-Logistic Model, among others
• System reliability evaluations, including parallel-series, series-parallel, and mixed parallel systems
• The concepts of time- and failure-dependent reliability within both repairable and non-repairable systems
• Parametric reliability models, including types of censoring, and the Exponential, Weibull, Lognormal, Gamma, Extreme Value, Half-Logistic, and Rayleigh Distributions

Preface xi

Prelude xv

Chapter 1 Reliability and Hazard Functions 1

1.1 Introduction 1

1.2 Reliability Definition and Estimation 5

1.3 Hazard Functions 16

1.4 Multivariate Hazard Rate 57

1.5 Competing Risk Model and Mixture of Failure Rates 60

1.6 Discrete Probability Distributions 68

1.7 Mean Time to Failure 71

1.8 Mean Residual Life 74

1.9 Time of First Failure 76

Problems 79

References 91

Chapter 2 System Reliability Evaluation 95

2.1 Introduction 95

2.2 Reliability Block Diagrams 96

2.3 Series Systems 99

2.4 Parallel Systems 101

2.5 Parallel–Series, Series–Parallel, and Mixed-Parallel Systems 103

2.6 Consecutive-k-out-of-n:F System 113

2.7 Reliability of k-out-of-n Systems 121

2.8 Reliability of k-out-of-n Balanced Systems 123

2.9 Complex Reliability Systems 125

2.10 Special Networks 143

2.11 Multistate Models 144

2.12 Redundancy 150

2.13 Importance Measures of Components 154

2.14 Weighted Importance Measures of Components 165

Problems 167

References 182

Chapter 3 Time- and Failure-Dependent Reliability 185

3.1 Introduction 185

3.2 Nonrepairable Systems 185

3.3 Mean Time to Failure 194

3.4 Repairable Systems 204

3.5 Availability 215

3.6 Dependent Failures 223

3.7 Redundancy and Standby 228

Problems 238

References 247

Chapter 4 Estimation Methods of the Parameters 251

4.1 Introduction 251

4.2 Method of Moments 252

4.3 The Likelihood Function 260

4.4 Method of Least Squares 278

4.5 Bayesian Approach 284

4.6 Bootstrap Method 288

4.7 Generation of Failure Time Data 290

Problems 292

References 298

Chapter 5 Parametric Reliability Models 301

5.1 Introduction 301

5.2 Approach 1: Historical Data 302

5.3 Approach 2: Operational Life Testing 303

5.4 Approach 3: Burn-in Testing 303

5.5 Approach 4: Accelerated Life Testing 304

5.6 Types of Censoring 305

5.7 The Exponential Distribution 308

5.8 The Rayleigh Distribution 322

5.9 The Weibull Distribution 331

5.10 The Lognormal Distribution 343

5.11 The Gamma Distribution 350

5.12 The Extreme Value Distribution 357

5.13 The Half-Logistic Distribution 360

5.14 The Frechet Distribution 367

5.15 The Birnbaum–Saunders Distribution 369

5.16 Linear Models 372

5.17 Multicensored Data 374

Problems 378

References 389

Chapter 6 Accelerated Life Testing 393

6.1 Introduction 393

6.2 Types of Reliability Testing 394

6.3 Accelerated Life Testing 403

6.4 ALT Models 406

6.5 Statistics-Based Models: Nonparametric 420

6.6 Physics-Statistics-Based Models 437

6.7 Physics-Experimental-Based Models 446

6.8 Degradation Models 449

6.9 Statistical Degradation Models 453

6.10 Accelerated Life Testing Plans 459

Problems 463

References 476

Chapter 7 Physics of Failures 481

7.1 Introduction 481

7.2 Fault Tree Analysis 481

7.3 Failure Modes and Effects Analysis 488

7.4 Stress–Strength Relationship 490

7.5 PoF: Failure Time Models 492

7.6 PoF: Degradation Models 512

Problems 519

References 524

Chapter 8 System Resilience 527

8.1 Introduction 527

8.2 Resilience Overview 528

8.3 Multi-Hazard 528

8.4 Resilience Modeling 532

8.5 Resilience Definitions and Attributes 535

8.6 Resilience Quantification 536

8.7 Importance Measures 542

8.8 Cascading Failures 544

8.9 Cyber Networks 546

Problems 557

References 559

Chapter 9 Renewal Processes and Expected Number of Failures 563

9.1 Introduction 563

9.2 Parametric Renewal Function Estimation 564

9.3 Nonparametric Renewal Function Estimation 578

9.4 Alternating Renewal Process 588

9.5 Approximations of M(t) 591

9.6 Other Types of Renewal Processes 594

9.7 The Variance of the Number of Renewals 595

9.8 Confidence Intervals for the Renewal Function 601

9.9 Remaining Life at Time t 604

9.10 Poisson Processes 606

9.11 Laplace Transform and Random Variables 609

Problems 611

References 619

Chapter 10 Maintenance and Inspection 621

10.1 Introduction 621

10.2 Preventive Maintenance and Replacement Models: Cost Minimization 622

10.3 Preventive Maintenance and Replacement Models: Downtime Minimization 631

10.4 Minimal Repair Models 634

10.5 Optimum Replacement Intervals for Systems Subject to Shocks 639

10.6 Preventive Maintenance and Number of Spares 642

10.7 Group Maintenance 649

10.8 Periodic Inspection 653

10.9 Condition-Based Maintenance 663

10.10 On-Line Surveillance and Monitoring 665

Problems 669

References 676

Chapter 11 Warranty Models 679

11.1 Introduction 679

11.2 Warranty Models for Nonrepairable Products 681

11.3 Warranty Models for Repairable Products 701

11.4 Two-Dimensional Warranty 716

11.5 Warranty Claims 718

Problems 725

References 731

Chapter 12 Case Studies 733

12.1 Case 1: A Crane Spreader Subsystem 733

12.2 Case 2: Design of a Production Line 739

12.3 Case 3: An Explosive Detection System 746

12.4 Case 4: Reliability of Furnace Tubes 752

12.5 Case 5: Reliability of Smart Cards 757

12.6 Case 6: Life Distribution of Survivors of Qualification and Certification 760

12.7 Case 7: Reliability Modeling of Telecommunication Networks for the Air Traffic Control System 767

12.8 Case 8: System Design Using Reliability Objectives 776

12.9 Case 9: Reliability Modeling of Hydraulic Fracture Pumps 786

12.10 Case 10: Availability of Medical Information Technology System 791

12.11 Case 11: Producer and Consumer Risk in System of Systems 797

References 804

Appendices

Appendix A Gamma Table 805

Appendix B Computer Program To Calculate the Reliability of a Consecutive-k-Out-of-n:F System 811

Appendix C Optimum Arrangement of Components In Consecutive-2-Out-of-N:F Systems 813

Appendix D Computer Program For Solving the Time-Dependent Equations 821

Appendix E The Newton–Raphson Method 823

Appendix F Coefficients of b_i’s For i = 1, …, n 829

Appendix G Variance of θ^∗₂’s In Terms of θ²₂/n and K₃/K^∗₂ 843

Appendix H Computer Listing of the Newton–Raphson Method 849

Appendix I Coefficients (a_i and b_i) of the Best Estimates of the Mean (μ) and Standard Deviation (σ) In Censored Samples Up To n = 20 From a Normal Population 851

Appendix J Baker’s Algorithm 865

Appendix K Standard Normal Distribution 869

Appendix L Critical Values of χ² 875

Appendix M Solutions of Selected Problems 879

Author Index 887

Subject 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.