Reliability Engineering and Risk Analysis : A Practical Guide

Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 6
Preface to the Third Edition......Page 14
Acknowledgments......Page 16
Authors......Page 18
1.2 Failure Models......Page 20
1.2.2 Damage–Endurance Model......Page 21
1.3 Failure Mechanisms......Page 22
1.4 Performance Measures......Page 26
1.5 Formal Definition of Reliability......Page 30
1.6 Definition of Availability......Page 31
References......Page 32
2.2.1 Sets and Boolean Algebra......Page 34
2.2.2 Basic Laws of Probability......Page 37
2.2.2.2 Frequency Interpretation of Probability......Page 38
2.2.2.4 Calculus of Probability......Page 39
2.2.3 Bayes’ Theorem......Page 43
2.3.1 Random Variable......Page 47
2.3.2.2 Binomial Distribution......Page 48
2.3.2.3 Hypergeometric Distribution......Page 50
2.3.2.4 Poisson’s Distribution......Page 51
2.3.2.5 Geometric Distribution......Page 52
2.3.3 Some Basic Continuous Distributions......Page 53
2.3.3.1 Normal Distribution......Page 55
2.3.3.2 Lognormal Distribution......Page 57
2.3.3.3 Exponential Distribution......Page 58
2.3.3.4 Weibull Distribution......Page 59
2.3.3.5 Gamma Distribution......Page 60
2.3.3.6 Beta Distribution......Page 61
2.3.4 Joint and Marginal Distributions......Page 62
2.3.5 Truncated Distributions......Page 65
2.4 Basic Characteristics of Random Variables......Page 66
2.5.1 Point Estimation......Page 72
2.5.1.1 Method of Moments......Page 73
2.5.1.2 Maximum Likelihood Method......Page 74
2.5.2 Interval Estimation and Hypothesis Testing......Page 75
2.5.2.1 Hypothesis Testing......Page 76
2.5.3 Bayesian Estimation......Page 77
2.6 Frequency Tables and Histograms......Page 78
2.7.1 Chi-Square Test......Page 80
2.7.2 Kolmogorov–Smirnov Test......Page 83
2.8 Regression Analysis......Page 84
2.8.1 Simple Linear Regression......Page 85
References......Page 93
3.1.1 Reliability Function......Page 94
3.1.2 Failure Rate......Page 96
3.1.3.1 Bounds Based on a Known Quantile......Page 101
3.2.1 Exponential Distribution......Page 102
3.2.2 Weibull Distribution......Page 103
3.2.3 Gamma Distribution......Page 104
3.2.4 Normal Distribution......Page 105
3.2.6.1 Some Basic Concepts and Definitions......Page 106
3.2.6.2 Order Statistics from Samples of Random Size......Page 107
3.2.6.4 Three Types of Limit Distributions......Page 108
3.3.1.1 Small Samples......Page 111
3.3.1.2 Large Samples......Page 112
3.3.2 Probability Plotting......Page 114
3.3.2.1 Exponential Distribution Probability Plotting......Page 115
3.3.2.2 Weibull Distribution Probability Plotting......Page 116
3.3.2.3 Normal and Lognormal Distribution Probability Plotting......Page 118
3.3.3 Total-Time-on-Test Plots......Page 120
3.4 Maximum Likelihood Estimation of Reliability Distribution Parameters......Page 122
3.4.1.2 Type I Censoring......Page 123
3.4.1.6 Maximum Likelihood Estimation Using Reliability Data......Page 124
3.4.2.3 Type II Life Test with Replacement......Page 128
3.4.2.4 Type II Life Test without Replacement......Page 129
3.4.3 Exponential Distribution Interval Estimation......Page 130
3.4.4 Lognormal Distribution......Page 133
3.4.5 Weibull Distribution......Page 134
3.4.6 Binomial Distribution......Page 137
3.5.1 Confidence Intervals for cdf and Reliability Function for Complete and Singly Censored Data......Page 138
3.5.2 Confidence Intervals for cdf and Reliability Function for Multiply Censored Data......Page 142
3.6 Bayesian Estimation Procedures......Page 144
3.6.1 Estimation of the Parameter of Exponential Distribution......Page 146
3.6.1.1 Selecting Parameters of Prior Distribution......Page 148
3.6.1.2 Uniform Prior Distribution......Page 150
3.6.2 Bayesian Estimation of the Parameter of Binomial Distribution......Page 152
3.6.2.1 Standard Uniform Prior Distribution......Page 153
3.6.2.2 Truncated Standard Uniform Prior Distribution......Page 154
3.6.2.3 Beta Prior Distribution......Page 155
3.6.2.5 Lognormal Prior Distribution......Page 159
3.6.3 Bayesian Estimation of the Weibull Distribution......Page 161
3.6.3.1 Prior Distribution......Page 162
3.6.3.4 Posterior Distribution of Weibull Distribution Parameters......Page 163
3.6.3.5 Particular Case......Page 167
3.6.4.1 Classical Simple Linear Regression......Page 168
3.6.4.2 Classical Probability Papers......Page 171
3.6.4.4 Including Prior Information about Model Parameters......Page 172
3.6.4.5 Including Prior Information about the Reliability or cdf......Page 175
3.7 Methods of Generic Failure Rate Determination......Page 177
References......Page 188
4.1.1 Series System......Page 192
4.1.2 Parallel Systems......Page 194
4.1.3 Standby Redundant Systems......Page 196
4.1.4 Load-Sharing Systems......Page 199
4.1.5 Complex Systems......Page 200
4.2.1 Fault Tree Method......Page 204
4.2.2.1 Analysis of Logic Trees Using Boolean Algebra......Page 207
4.2.2.2 Combinatorial (Truth Table) Technique for Evaluation of Logic Trees......Page 212
4.2.2.3 Binary Decision Diagrams......Page 215
4.2.3 Success Tree Method......Page 222
4.3 Event Tree Method......Page 223
4.3.1 Construction of Event Trees......Page 224
4.3.2 Evaluation of Event Trees......Page 225
4.4 Master Logic Diagram......Page 226
4.5.1 Types of FMEA......Page 233
4.5.3.1 FMEA for Aerospace Applications......Page 234
4.5.3.2 FMEA for Transportation Applications......Page 237
4.5.4 FMECA Procedure: Criticality Analysis......Page 245
References......Page 261
5.1.1 Basics of Point Processes......Page 262
5.1.2 Homogeneous Poisson Process......Page 265
5.1.3 Renewal Process......Page 266
5.1.4 Nonhomogeneous Poisson Process......Page 269
5.1.5 General Renewal Process......Page 271
5.1.6 Probabilistic Bounds......Page 276
5.1.7.3 Estimation Based on One Realization (Grouped Data)......Page 280
5.1.7.5 Confidence Limits for CIF......Page 282
5.1.8.1 Procedures Based on the Poisson Distribution......Page 286
5.1.8.2 Procedures Based on the Exponential Distribution of Time Intervals......Page 288
5.1.9 Data Analysis for the NHPP......Page 289
5.1.9.1 Regression Analysis of Time Intervals......Page 290
5.1.9.2 Maximum Likelihood Procedures......Page 292
5.1.9.3 Laplace’s Test......Page 294
5.1.10 Data Analysis for GRP......Page 297
5.1.10.2 Example Based on Real Data......Page 298
5.2 Availability of Repairable Systems......Page 299
5.2.1 Instantaneous (Point) Availability......Page 300
5.2.4 Availability Measures Based on Causes of Unavailability......Page 304
5.3 Use of Markov Processes for Determining System Availability......Page 305
5.4 Use of System Analysis Techniques in the Availability Calculations of Complex Systems......Page 311
References......Page 323
6.1 Probabilistic Physics-of-Failure Reliability Modeling......Page 326
6.1.1 Stress–Strength Model......Page 327
6.1.2 Damage–Endurance Model......Page 330
6.1.3 Performance–Requirement Model......Page 336
6.2.1 Introduction......Page 337
6.2.2.1 Classification......Page 338
6.2.3 Software Life Cycle Models......Page 342
6.3 Human Reliability......Page 343
6.3.1 HRA Process......Page 344
6.3.2.1 Simulation Methods......Page 347
6.3.2.2 Expert Judgment Methods......Page 348
6.3.2.3 Analytical Methods......Page 349
6.3.3 Human Reliability Data......Page 353
6.4.1 Birnbaum Measure of Importance......Page 354
6.4.2 Criticality Importance......Page 355
6.4.3 Fussell–Vesely Importance......Page 356
6.4.5 RAW Importance......Page 357
6.4.6 Practical Aspects of Importance Measures......Page 360
6.5.1 Reliability-Centered Maintenance......Page 361
6.5.2 Optimal Preventive Maintenance Scheduling......Page 364
6.5.3 Comparative Analysis of Optimal Maintenance Policies under General Repair with Underlying Weibull Distributions......Page 365
6.6.2 Duane Method......Page 367
6.6.3 Army Material Systems Analysis Activity Method......Page 370
References......Page 375
7.1.1.2 AL Model......Page 380
7.1.2 Some Popular AL (Reliability) Models......Page 382
7.1.3.2 Two-Sample Criterion......Page 384
7.1.3.5 Quantile–Quantile Plots......Page 386
7.1.3.6 Reliability Models Fitting: Constant Stress Case......Page 387
7.1.4 AL Model for Time-Dependent Stress......Page 388
7.1.4.1 AL Reliability Model for Time-Dependent Stress and Palmgren–Miner’s Rule......Page 390
7.1.5.1 Statistical Estimation of AL Reliability Models on the Basis of AL Tests with Time-Dependent Stress......Page 391
7.1.6 PH Model Data Analysis......Page 392
7.1.6.3 PH Model and Data Analysis......Page 393
7.2.1 Introduction......Page 395
7.2.2.1 Models for Nonrepairable Systems......Page 396
7.2.2.3 Bivariate Models......Page 397
7.2.3.1 Nonrepairable System Models......Page 398
7.2.3.2 Repairable System Models......Page 400
7.2.4.1 Survival Regression in Root Cause Analysis of Field Failures......Page 401
7.2.4.2 Life Scales: Time versus Usage......Page 403
7.2.4.3 Warranty Data Maturity Issues......Page 405
7.2.4.4 Calendarized Warranty Forecasting......Page 407
7.3 Analysis of Dependent Failures......Page 408
7.3.1 Single-Parameter Models......Page 410
7.3.2.1 Multiple Greek Letter Model......Page 413
7.3.2.3 BFR Model......Page 415
7.3.3 Data Analysis for CCFs......Page 416
7.4 Uncertainty Analysis......Page 418
7.4.1.2 Model Uncertainties......Page 419
7.4.2.1 Method of Moments......Page 420
7.4.3.1 Lloyd–Lipow Method......Page 424
7.4.4.1 Classical Monte Carlo Simulation......Page 426
7.4.4.3 Bootstrap Method......Page 427
7.5 Use of Expert Opinion for Estimating Reliability Parameters......Page 431
7.5.1 Geometric Averaging Technique......Page 434
7.5.3 Statistical Evidence on the Accuracy of Expert Estimates......Page 435
References......Page 441
8.1 Determination of Risk Values......Page 446
8.2 Quantitative Risk Assessment......Page 448
8.2.3 Identification of Challenges to Barriers......Page 449
8.3 Probabilistic Risk Assessment......Page 450
8.3.2.1 Objectives and Methodology......Page 451
8.3.2.2 Familiarization and Information Assembly......Page 452
8.3.2.3 Identification of Initiating Events......Page 453
8.3.2.4 Sequence or Scenario Development......Page 454
8.3.2.5 Logic Modeling......Page 455
8.3.2.6 Failure Data Collection, Analysis, and Performance Assessment......Page 456
8.3.2.7 Quantification and Integration......Page 457
8.3.2.8 Uncertainty Analysis......Page 458
8.3.2.10 Risk Ranking and Importance Analysis......Page 459
8.4.1 Primary CNG Fire Hazards......Page 461
8.4.6 Storage Cascade......Page 462
8.4.9 Gas Release Scenarios......Page 463
8.4.11 Gas Release......Page 465
8.4.14 Consequence Determination......Page 466
8.4.17 Summary of PRA Results......Page 467
8.4.19 Uncertainty Analysis......Page 468
8.4.20 Sensitivity and Importance Analysis......Page 469
8.5 A Simple Fire Protection Risk Analysis......Page 470
8.6.1 Introduction......Page 477
8.6.2 Basic Methodology......Page 479
8.6.3 Differences between APA and PRAs......Page 480
References......Page 483
Appendix A: Statistical Tables......Page 486
Appendix B: Generic Failure Probability Data......Page 500
Index......Page 512