An introdution to reliability and maintainability engineering

Title Page......Page 3
Contents......Page 5
Preface......Page 13
Course Software......Page 16
Chapter 1: Introduction......Page 17
  1.1.1 Reliability Improvement......Page 19
  1.1.2 Random versus Deterministic Failure Phenomena......Page 20
 1.2 Concepts, Terms, and Definitions......Page 21
 1.3 Applications......Page 23
 1.4 A Brief History......Page 26
 1.5 Scope of the Text......Page 27
  1A.1 Random Events......Page 29
  1A.3 Random Variables......Page 32
  1A.4 Discrete Distributions......Page 33
  1A.6 Poisson Distribution......Page 34
  1A.7 Continuous Distributions......Page 35
PART 1: Basic Reliability Models......Page 37
  2.1 The Reliability Function......Page 39
  2.2 Mean Time to Failure......Page 42
  2.3 Hazard Rate Function......Page 44
  2.4 Bathtub Curve......Page 47
  2.5 Conditional Reliability......Page 48
  2.6 Summary......Page 50
  Appendix 2A: Derivation of Equation (2.8)......Page 51
  Appendix 2C: Conditional Reliability and Failure Rates......Page 52
  Appendix 2D: Intermediate Calculations for the Linear Bathtub Curve......Page 53
  Exercises......Page 54
  3.1 The Exponential Reliability Function......Page 60
  3.2 Failure Modes......Page 64
   3.2.1 Failure Modes with CFR Model......Page 65
  3.3 Applications......Page 66
   3.3.2 Repetitive Loading......Page 67
   3.3.3 Reliability Bounds......Page 69
  3.4 The Two-Parameter Exponential Distribution......Page 70
  3.5 Poisson Process......Page 71
  3.6 Redundancy and the CFR Model......Page 73
  Exercises......Page 75
  4.1 The Weibull Distribution......Page 79
   4.1.1 Design Life, Median, and Mode......Page 84
   4.1.3 Failure Modes......Page 86
   4.1.4 Identical Weibull Components......Page 87
   4.1.5 The Three-Parameter Weibull......Page 88
   4.1.6 Redundancy with Weibull Failures......Page 89
   4.1.7 The Minimum Extreme Value Distribution......Page 90
  4.2 The Normal Distribution......Page 92
  4.3 The Lognormal Distribution......Page 96
  4.4 The Gamma Distribution......Page 100
  Appendix 4A: Derivation of the MTTF for the Weibull Distribution......Page 103
  Appendix 4B: Derivation of the Mode for the Weibull Distribution......Page 104
  Appendix 4D: Hazard Rate for the Two-Component Weibull Redundant System......Page 105
  Exercises......Page 106
  5.1 Serial Configuration......Page 114
  5.2 Parallel Configuration......Page 116
   5.3.1 High-Level versus Low-Level Redundancy......Page 118
   5.3.2 k-out-of-n Redundancy......Page 120
   5.3.3 Complex Configurations......Page 121
  5.4 System Structure Function, Minimal Cuts, and Minimal Paths (Optional)......Page 124
   5.4.2 Minimal Path and Cut Sets......Page 125
   5.4.3 System Bounds......Page 126
  5.5 Common-Mode Failures......Page 128
  5.6 Three-State Devices......Page 129
   5.6.2 Parallel Structure......Page 130
   5.6.3 Low-Level Redundancy......Page 131
   5.6.4 High-Level Redundancy......Page 132
  Exercises......Page 133
  6.1 Markov Analysis......Page 142
  6.2 Load-Sharing System......Page 145
  6.3 Standby Systems......Page 146
   6.3.1 Identical Standby Units......Page 148
   6.3.3 Three-Component Standby System......Page 149
  6.4 Degraded Systems......Page 151
  6.5 Three-State Devices......Page 152
  Appendix 6A: Solution to Two-Component Redundant System......Page 153
  Appendix 6C: Solution to Standby System Model......Page 154
  Exercises......Page 155
  7.1 Covariate Models......Page 160
   7.1.1 Proportional Hazards Models......Page 161
   7.1.2 Location-Scale Models......Page 163
  7.2 Static Models......Page 164
   7.2.1 Random Stress and Constant Strength......Page 165
   7.2.3 Random Stress and Random Strength......Page 166
   7.2.4 Mixed Distributions with Analytical Solutions......Page 171
   7.3.1 Periodic Loads......Page 172
   7.3.2 Random Loads......Page 173
   7.3.3 Random Fixed Stress and Strength......Page 174
  7.4 Physics-of-Failure Models......Page 175
  Exercises......Page 178
 Chapter 8: Design for Reliability......Page 187
  8.1 Reliability Specification and System Measurements......Page 189
   8.1.1 System Effectiveness......Page 190
   8.1.2 Economic Analysis and Life-Cycle Costs......Page 191
  8.2 Reliability Allocation......Page 193
   8.2.2 Optimal Allocations......Page 194
   8.2.3 ARINC Method......Page 196
   8.2.4 AGREE Method......Page 197
   8.2.5 Redundancies......Page 198
   8.3.1 Parts and Material Selection......Page 199
   8.3.2 Derating......Page 202
   8.3.3 Stress-Strength Analysis......Page 203
   8.3.4 Complexity and Technology......Page 205
   8.3.5 Redundancy......Page 206
  8.4 Failure Analysis......Page 208
   8.4.2 Identification of Failure Modes......Page 211
   8.4.3 Determination of Cause......Page 212
   8.4.4 Assessment of Effect......Page 213
   8.4.5 Estimation of Probability of Occurrence......Page 214
   8.4.7 Classification of Severity......Page 215
   8.4.9 Determination of Corrective Action......Page 217
  8.5 System Safety and Fault Tree Analysis......Page 218
   8.5.1 Fault Tree Analysis......Page 219
   8.5.2 Minimal Cut Sets......Page 223
   8.5.3 Quantitative Analysis......Page 226
  Exercises......Page 228
  9.1 Analysis of Downtime......Page 235
  9.2 The Repair-Time Distribution......Page 237
   9.2.2 Lognormal Repair Times......Page 238
   9.3.1 Renewal Process......Page 240
   9.3.2 Minimal Repair Process......Page 245
   9.3.3 Overhaul and Cycle Time......Page 250
  9.4 System Repair Time......Page 252
  9.5 Reliability under Preventive Maintenance......Page 253
  9.6 State-Dependent Systems with Repair......Page 257
  Appendix 9A: The MTTF for the Preventive Maintenance Model......Page 260
  Appendix 9C: Solution to Standby System with Repair......Page 261
  Appendix 9D: System MTTR Derivation under Simultaneous Repair (Table 9.1)......Page 262
  Exercises......Page 263
 Chapter 10: Design for Maintainability......Page 270
   10.1.1 Measurements and Specifications......Page 271
   10.1.2 Maintenance Concepts and Procedures......Page 273
   10.1.3 Component Reliability and Maintainability......Page 276
   10.2.1 Fault Isolation and Self-Diagnostics......Page 277
   10.2.2 Parts Standardization and Interchangeability......Page 278
   10.2.3 Modularization and Accessibility......Page 279
   10.2.4 Repair versus Replacement......Page 280
   10.2.5 Proactive Maintenance......Page 283
  10.3 Human Factors and Ergonomics......Page 287
  10.4 Maintainability Prediction and Demonstration......Page 289
   10.4.2 Maintainability Demonstration......Page 290
  Exercises......Page 293
  11.1 Concepts and Definitions......Page 299
   11.1.2 Achieved Availability......Page 300
   11.1.3 Operational Availability......Page 301
   11.1.5 Availability with Minimal Repair......Page 302
  11.2 Exponential Availability Model......Page 303
  11.3 System Availability......Page 304
   11.3.1 Availability with Standby Systems......Page 305
   11.3.2 Steady-State Availability......Page 306
   11.3.3 Matrix Approach......Page 308
  11.4 Inspection and Repair Availability Model......Page 310
  Appendix 11A: Solution to Single Unit with Repair Model......Page 312
  Exercises......Page 313
PART 2: The Analysis of Failure Data......Page 319
  12.1 Data Collection......Page 321
   12.2.1 Ungrouped Complete Data......Page 324
   12.2.2 Grouped Complete Data......Page 330
   12.2.3 Ungrouped Censored Data......Page 334
   12.2.4 Grouped Censored Data......Page 338
  12.3 Static Life Estimation......Page 340
  12.4 Nonparametric Confidence Intervals......Page 342
  Exercises......Page 344
  13.1 Product Testing......Page 350
  13.2 Reliability Life Testing......Page 351
  13.3 Test Time Calculations......Page 352
   13.3.1 Length of Test......Page 353
  13.4 Burn-In Testing......Page 354
  13.5 Acceptance Testing......Page 357
   13.5.1 Binomial Acceptance Testing......Page 358
   13.5.2 Sequential Tests......Page 360
  13.6 Accelerated Life Testing......Page 365
   13.6.2 Time Compression......Page 366
   13.6.3 Constant-Stress Models......Page 368
   13.6.4 Other Acceleration Models......Page 372
  13.7 Competing Failure Modes......Page 376
  Appendix 13A: Derivation of Expected Test Time......Page 377
  Appendix 13B: Expected Test Time (Type II Testing)......Page 378
  Exercises......Page 379
  14.1 Reliability Growth Process......Page 385
  14.2 Idealized Growth Curve......Page 386
  14.3 Duane Growth Model......Page 388
  14.4 AMSAA Model......Page 392
   14.4.1 Parameter Estimation for the Power Law Intensity Function......Page 393
   14.4.2 Parameter Estimation with Grouped Data......Page 396
  14.5 Other Growth Models......Page 397
  Exercises......Page 399
 Chapter 15: Identifying Failure and Repair Distributions......Page 404
  15.1 Identifying Candidate Distributions......Page 405
  15.2 Probability Plots and Least-Squares Curve-Fitting......Page 408
   15.2.1 Exponential Plots......Page 409
   15.2.2 Weibull Plots......Page 410
   15.2.3 Normal Plots......Page 416
   15.2.4 Lognormal Plots......Page 417
   15.2.5 Multiply Censored Time Plots......Page 418
   15.2.6 Curve Fitting for the Minimum Extreme-Value Distribution......Page 421
  15.3 Parameter Estimation......Page 422
   15.3.1 Maximum Likelihood Estimator......Page 423
   15.3.2 Exponential MLE......Page 424
   15.3.4 Normal and Lognormal MLEs......Page 425
   15.3.5 Maximum Likelihood Estimation with Multiply Censored Data......Page 426
   15.3.6 Location Parameter Estimation......Page 428
   15.3.7 Parameter Estimation for the Minimum Extreme-Value Distribution......Page 429
   15.3.8 Parameter Estimation for the Gamma Distribution......Page 431
   15.3.9 Parameter Estimation for Interval Data......Page 433
   15.4.1 Confidence Intervals for the Constant Failure Rate Model......Page 435
   15.4.2 Confidence Intervals for Other Distributions......Page 438
  15.5 Parameter Estimation for Covariate Models......Page 441
  Appendix 15A: Weibull Maximum Likelihood Estimator......Page 443
  Appendix 15C: MLE for Normal and Lognormal Distributions with Censored Data......Page 444
  Appendix 15D: MLE for Gamma Distribution with Multiply Censored Data......Page 445
  Exercises......Page 446
 Chapter 16: Statistical Tests......Page 451
  16.1 Chi-Square Goodness-of-Fit Test......Page 452
  16.2 Bartlett’s Test for the Exponential Distribution......Page 459
  16.3 Mann’s Test for the Weibull Distribution......Page 460
  16.4 Kolmogorov-Smirnov Test for Normal and Lognormal Distributions......Page 462
  16.5 Tests for the Power-Law Process Model......Page 464
  16.6 On Fitting Distributions......Page 468
  Exercises......Page 469
PART 3: Application......Page 475
  17.1 Case 1: Redundancy......Page 477
  17.2 Case 2: Burn-In Testing......Page 479
  17.3 Case 3: Preventive Maintenance Analysis......Page 482
  17.4 Case 4: Reliability Allocation......Page 485
  17.5 Case 5: Reliability Growth Testing......Page 487
  17.6 Case 6: Repairable System Analysis......Page 488
  17.7 Case 7: Multiply Censored Data......Page 490
  17.8 Case 8: Multiple Failure Modes......Page 492
  17.9 Case 9: Availability......Page 495
  Exercises (Mini-Cases)......Page 497
  18.1 Objectives, Functions, and Processes......Page 502
  18.2 The Economics of Reliability and Maintainability and System Design......Page 503
   18.2.1 Life-Cycle Cost Model......Page 505
   18.2.2 Minimal Repair......Page 509
  18.3 Organizational Considerations......Page 510
  18.4 Data Sources and Data Collection Methods......Page 512
   18.4.1 Field Data......Page 513
   18.4.3 External Data Sources......Page 516
  18.5 Product Liability, Warranties, and Related Matters......Page 518
  18.6 Software Reliability......Page 520
References......Page 523
Appendix......Page 529
Index......Page 553