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 Parallelâ"Series, Seriesâ"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 Birnbaumâ"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 Stressâ"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 Newtonâ"Raphson Method 823
Appendix F Coefficients of biâs For i = 1, â¦, n 829
Appendix G Variance of θâ-2âs In Terms of θ22/n and K3/Kâ-2 843
Appendix H Computer Listing of the Newtonâ"Raphson Method 849
Appendix I Coefficients (ai and bi) of the Best Estimates of the Mean (μ) and Standard Deviation (Ï) In Censored Samples Up To n = 20 From a Normal Population 851
Appendix J Bakerâs Algorithm 865
Appendix K Standard Normal Distribution 869
Appendix L Critical Values of Ï2 875
Appendix M Solutions of Selected Problems 879
Author Index 887
Subject Index 895
