Title Details

Elsayed A. Elsayed, PhD, is a professor in the Department of Industrial and Systems Engineering, Rutgers University, and the Director of the NSF/Industry/University Co-operative Research Center for Quality and Reliability Engineering. He is the recipient of the Institute of Industrial Engineers (IIE) Fellow Award, an ASME Fellow, the Senior Fulbright Award, and the 2011 Thomas Alva Edison Patent Award. He is a coauthor of Quality Engineering in Production Systems and the author of Reliability Engineering, which received the 1990 and 1997 IIE/Joint Publishers Book-of-the-Year Award respectively.

Preface xi

Prelude xiv

Chapter 1 Reliability and Hazard Functions 1

1.1 Introduction 1

1.2 Reliability Definition and Estimation 3

1.3 Hazard Functions 15

1.4 Multivariate Hazard Rate 55

1.5 Competing Risk Model and Mixture of Failure Rates 59

1.6 Discrete Probability Distributions 64

1.7 Mean Time to Failure 67

1.8 Mean Residual Life (MRL) 70

1.9 Time of First Failure 71

Problems 73

References 85

Chapter 2 System Reliability Evaluation 87

2.1 Introduction 87

2.2 Reliability Block Diagrams 87

2.3 Series Systems 91

2.4 Parallel Systems 93

2.5 Parallel-Series, Series-Parallel, and Mixed-Parallel Systems 95

2.6 Consecutive-k-out-of-n:F System 104

2.7 Reliability of k-out-of-n Systems 113

2.8 Reliability of k-out-of-n Balanced Systems 115

2.9 Complex Reliability Systems 117

2.10 Special Networks 131

2.11 Multistate Models 132

2.12 Redundancy 138

2.13 Importance Measures of Components 142

Problems 154

References 167

Chapter 3 Time- and Failure-Dependent Reliability 170

3.1 Introduction 170

3.2 Nonrepairable Systems 170

3.3 Mean Time to Failure (MTTF) 178

3.4 Repairable Systems 187

3.5 Availability 198

3.6 Dependent Failures 207

3.7 Redundancy and Standby 212

Problems 222

References 231

Chapter 4 Estimation Methods of the Parameters of Failure-Time Distributions 233

4.1 Introduction 233

4.2 Method of Moments 234

4.3 The Likelihood Function 241

4.4 Method of Least Squares 256

4.5 Bayesian Approach 261

4.6 Generation of Failure-Time Data 265

Problems 267

References 272

Chapter 5 Parametric Reliability Models 273

5.1 Introduction 273

5.2 Approach 1: Historical Data 273

5.3 Approach 2: Operational Life Testing 274

5.4 Approach 3: Burn-In Testing 275

5.5 Approach 4: Accelerated Life Testing 275

5.6 Types of Censoring 277

5.7 The Exponential Distribution 279

5.8 The Rayleigh Distribution 294

5.9 The Weibull Distribution 302

5.10 Lognormal Distribution 314

5.11 The Gamma Distribution 321

5.12 The Extreme Value Distribution 329

5.13 The Half-Logistic Distribution 331

5.14 Frechet Distribution 338

5.15 Birnbaum–Saunders Distribution 341

5.16 Linear Models 344

5.17 Multicensored Data 346

Problems 351

References 361

Chapter 6 Models for Accelerated Life Testing 364

6.1 Introduction 364

6.2 Types of Reliability Testing 365

6.3 Accelerated Life Testing 368

6.4 ALT Models 372

6.5 Statistics-Based Models: Nonparametric 386

6.6 Physics-Statistics-Based Models 404

6.7 Physics-Experimental-Based Models 412

6.8 Degradation Models 415

6.9 Statistical Degradation Models 419

6.10 Accelerated Life Testing Plans 421

Problems 425

References 436

Chapter 7 Renewal Processes and Expected Number of Failures 440

7.1 Introduction 440

7.2 Parametric Renewal Function Estimation 441

7.3 Nonparametric Renewal Function Estimation 455

7.4 Alternating Renewal Process 465

7.5 Approximations of M(t ) 468

7.6 Other Types of Renewal Processes 469

7.7 The Variance of Number of Renewals 471

7.8 Confidence Intervals for the Renewal Function 477

7.9 Remaining Life at Time T 479

7.10 Poisson Processes 481

7.11 Laplace Transform and Random Variables 485

Problems 487

References 494

Chapter 8 Preventive Maintenance and Inspection 496

8.1 Introduction 496

8.2 Preventive Maintenance and Replacement Models: Cost Minimization 497

8.3 Preventive Maintenance and Replacement Models: Downtime Minimization 506

8.4 Minimal Repair Models 509

8.5 Optimum Replacement Intervals for Systems Subject to Shocks 513

8.6 Preventive Maintenance and Number of Spares 517

8.7 Group Maintenance 524

8.8 Periodic Inspection 527

8.9 Condition-Based Maintenance 535

8.10 Online Surveillance and Monitoring 537

Problems 542

References 548

Chapter 9 Warranty Models 551

9.1 Introduction 551

9.2 Warranty Models for Nonrepairable Products 553

9.3 Warranty Models for Repairable Products 574

9.4 Two-Dimensional Warranty 588

9.5 Warranty Claims 590

Problems 597

References 601

Chapter 10 Case Studies 603

10.1 Case 1: A Crane Spreader Subsystem 603

10.2 Case 2: Design of a Production Line 609

10.3 Case 3: An Explosive Detection System 617

10.4 Case 4: Reliability of Furnace Tubes 623

10.5 Case 5: Reliability of Smart Cards 629

10.6 Case 6: Life Distribution of Survivors of Qualification and Certification 632

10.7 Case 7: Reliability Modeling of Telecommunication Networks for the Air Traffic Control System 639

10.8 Case 8: System Design Using Reliability Objectives 648

10.9 Case 9: Reliability Modeling of Hydraulic Fracture Pumps 658

References 663

Appendices

Appendix A Gamma Table 667

Appendix B Computer Program to Calculate the Reliability of a Consecutive-k-out-of-n:F System 674

Appendix C Optimum Arrangement of Components in Consecutive-2-out-of-n:F Systems 676

Appendix D Computer Program for Solving the Time-Dependent Equations Using Runge-Kutta’s Method 682

Appendix E The Newton–Raphson Method 684

Appendix F Coefficients of b_i’s for i = 1, . . . , n 689

Appendix G Variance of Ө ^∗₂’s in Terms of Ө ²₂/n and K₃ /K^*₂ 716

Appendix H Computer Listing of the Newton–Raphson Method 722

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 724

Appendix J Baker’s Algorithm 737

Appendix K Standard Normal Distribution 741

Appendix L Critical Values of χ2 747

Appendix M Solutions of Selected Problems 750

Author Index 759

Subject Index 764

“The well written book may be used as a reference work for practitioners and as a textbook for courses in reliability engineering, where knowledge in probability calculus and statistics is presumed.”  (Zentralblatt MATH, 1 December 2012) 

“I recommend this book for graduate courses, as it is clear and complete, and treats a vital 21st century problem.”  (Computing Reviews, 29 November 2012)