كتاب Handbook of Reliability Engineering - Hoang Pham
منتدى هندسة الإنتاج والتصميم الميكانيكى
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 كتاب Handbook of Reliability Engineering - Hoang Pham

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تاريخ التسجيل : 01/07/2009
العمر : 30
الدولة : مصر
العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
الجامعة : المنوفية

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Handbook of Reliability Engineering
Hoang Pham

كتاب  Handbook of Reliability Engineering - Hoang Pham P_708t077t1
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Contents
PART I. System Reliability and Optimization
1 Multi-state k-out-of-n Systems
Ming J. Zuo, Jinsheng Huang and Way Kuo . 3
1.1 Introduction 3
1.2 Relevant Concepts in Binary Reliability Theory . 3
1.3 Binary k-out-of-n Models . 4
1.3.1 The k-out-of-n:G System with Independently and Identically
Distributed Components . 5
1.3.2 Reliability Evaluation Using Minimal Path or Cut Sets . 5
1.3.3 Recursive Algorithms 6
1.3.4 Equivalence Between a k-out-of-n:G System and an
(n ? k + 1)-out-of-n:F system 6
1.3.5 The Dual Relationship Between the k-out-of-n G and F Systems 7
1.4 Relevant Concepts in Multi-state Reliability Theory 8
1.5 A Simple Multi-state k-out-of-n:G Model 10
1.6 A Generalized Multi-state k-out-of-n:G System Model . 11
1.7 Properties of Generalized Multi-state k-out-of-n:G Systems 13
1.8 Equivalence and Duality in Generalized Multi-state k-out-of-n Systems 15
2 Reliability of Systems with Multiple Failure Modes
Hoang Pham . 19
2.1 Introduction 19
2.2 The Series System . 20
2.3 The Parallel System 21
2.3.1 Cost Optimization 21
2.4 The Parallel–Series System 22
2.4.1 The Profit Maximization Problem 23
2.4.2 Optimization Problem 24
2.5 The Series–Parallel System 25
2.5.1 Maximizing the Average System Profit . 26
2.5.2 Consideration of Type I Design Error 27
2.6 The k-out-of-n Systems 27
2.6.1 Minimizing the Average System Cost 29
2.7 Fault-tolerant Systems 32
2.7.1 Reliability Evaluation 33xii Contents
2.7.2 Redundancy Optimization 34
2.8 Weighted Systems with Three Failure Modes 34
3 Reliabilities of Consecutive-k Systems
Jen-Chun Chang and Frank K. Hwang 37
3.1 Introduction 37
3.1.1 Background 37
3.1.2 Notation . 38
3.2 Computation of Reliability 39
3.2.1 The Recursive Equation Approach . 39
3.2.2 The Markov Chain Approach 40
3.2.3 Asymptotic Analysis . 41
3.3 Invariant Consecutive Systems 41
3.3.1 Invariant Consecutive-2 Systems 41
3.3.2 Invariant Consecutive-k Systems 42
3.3.3 Invariant Consecutive-k G System 43
3.4 Component Importance and the Component Replacement Problem . 43
3.4.1 The Birnbaum Importance 44
3.4.2 Partial Birnbaum Importance 45
3.4.3 The Optimal Component Replacement . 45
3.5 The Weighted-consecutive-k-out-of-n System 47
3.5.1 The Linear Weighted-consecutive-k-out-of-n System . 47
3.5.2 The Circular Weighted-consecutive-k-out-of-n System 47
3.6 Window Systems . 48
3.6.1 The f -within-consecutive-k-out-of-n System . 49
3.6.2 The 2-within-consecutive-k-out-of-n System 51
3.6.3 The b-fold-window System . 52
3.7 Network Systems . 53
3.7.1 The Linear Consecutive-2 Network System . 53
3.7.2 The Linear Consecutive-k Network System . 54
3.7.3 The Linear Consecutive-k Flow Network System 55
3.8 Conclusion 57
4 Multi-state System Reliability Analysis and Optimization
G. Levitin and A. Lisnianski . 61
4.1 Introduction 61
4.1.1 Notation . 63
4.2 Multi-state System Reliability Measures . 63
4.3 Multi-state System Reliability Indices Evaluation Based on the
Universal Generating Function 64
4.4 Determination of u-function of Complex Multi-state System Using
Composition Operators 67
4.5 Importance and Sensitivity Analysis of Multi-state Systems 68
4.6 Multi-state System Structure Optimization Problems 72
4.6.1 Optimization Technique . 73
4.6.1.1 Genetic Algorithm 73Contents xiii
4.6.1.2 Solution Representation and Decoding Procedure . 75
4.6.2 Structure Optimization of Series–Parallel System with
Capacity-based Performance Measure . 75
4.6.2.1 Problem Formulation . 75
4.6.2.2 Solution Quality Evaluation . 76
4.6.3 Structure Optimization of Multi-state System with Two Failure
Modes . 77
4.6.3.1 Problem Formulation . 77
4.6.3.2 Solution Quality Evaluation . 80
4.6.4 Structure Optimization for Multi-state System with Fixed
Resource Requirements and Unreliable Sources 83
4.6.4.1 Problem Formulation . 83
4.6.4.2 Solution Quality Evaluation . 84
4.6.4.3 The Output Performance Distribution of a System
Containing Identical Elements in the Main
Producing Subsystem . 85
4.6.4.4 The Output Performance Distribution of a System
Containing Different Elements in the Main
Producing Subsystem . 85
4.6.5 Other Problems of Multi-state System Optimization 87
5 Combinatorial Reliability Optimization
C. S. Sung, Y. K. Cho and S. H. Song . 91
5.1 Introduction 91
5.2 Combinatorial Reliability Optimization Problems of Series Structure . 95
5.2.1 Optimal Solution Approaches 95
5.2.1.1 Partial Enumeration Method . 95
5.2.1.2 Branch-and-bound Method 96
5.2.1.3 Dynamic Programming 98
5.2.2 Heuristic Solution Approach 99
5.3 Combinatorial Reliability Optimization Problems of a Non-series
Structure . 102
5.3.1 Mixed Series–Parallel System Optimization Problems . 102
5.3.2 General System Optimization Problems 106
5.4 Combinatorial Reliability Optimization Problems with
Multiple-choice Constraints . 107
5.4.1 One-dimensional Problems . 108
5.4.2 Multi-dimensional Problems 111
5.5 Summary . 113
PART II. Statistical Reliability Theory
6 Modeling the Observed Failure Rate
M. S. Finkelstein . 117
6.1 Introduction 117
6.2 Survival in the Plane . 118xiv Contents
6.2.1 One-dimensional Case 118
6.2.2 Fixed Obstacles 119
6.2.3 Failure Rate Process . 121
6.2.4 Moving Obstacles . 122
6.3 Multiple Availability . 124
6.3.1 Statement of the Problem 124
6.3.2 Ordinary Multiple Availability 125
6.3.3 Accuracy of a Fast Repair Approximation 126
6.3.4 Two Non-serviced Demands in a Row 127
6.3.5 Not More than N Non-serviced Demands . 129
6.3.6 Time Redundancy 130
6.4 Modeling the Mixture Failure Rate 132
6.4.1 Definitions and Conditional Characteristics 132
6.4.2 Additive Model 133
6.4.3 Multiplicative Model . 133
6.4.4 Some Examples 135
6.4.5 Inverse Problem . 136
7 Concepts of Stochastic Dependence in Reliability Analysis
C. D. Lai and M. Xie . 141
7.1 Introduction 141
7.2 Important Conditions Describing Positive Dependence 142
7.2.1 Six Basic Conditions . 143
7.2.2 The Relative Stringency of the Conditions . 143
7.2.3 Positive Quadrant Dependent in Expectation 144
7.2.4 Associated Random Variables 144
7.2.5 Positively Correlated Distributions . 145
7.2.6 Summary of Interrelationships . 145
7.3 Positive Quadrant Dependent Concept . 145
7.3.1 Constructions of Positive Quadrant Dependent Bivariate
Distributions . 146
7.3.2 Applications of Positive Quadrant Dependence Concept to
Reliability . 146
7.3.3 Effect of Positive Dependence on the Mean Lifetime of a
Parallel System 146
7.3.4 Inequality Without Any Aging Assumption . 147
7.4 Families of Bivariate Distributions that are Positive Quadrant
Dependent . 147
7.4.1 Positive Quadrant Dependent Bivariate Distributions with
Simple Structures 148
7.4.2 Positive Quadrant Dependent Bivariate Distributions with
More Complicated Structures 149
7.4.3 Positive Quadrant Dependent Bivariate Uniform Distributions 150
7.4.3.1 Generalized Farlie–Gumbel–Morgenstern Family of
Copulas 151
7.5 Some Related Issues on Positive Dependence 152Contents xv
7.5.1 Examples of Bivariate Positive Dependence Stronger than
Positive Quadrant Dependent Condition 152
7.5.2 Examples of Negative Quadrant Dependence 153
7.6 Positive Dependence Orderings . 153
7.7 Concluding Remarks . 154
8 Statistical Reliability Change-point Estimation Models
Ming Zhao 157
8.1 Introduction 157
8.2 Assumptions in Reliability Change-point Models 158
8.3 Some Specific Change-point Models . 159
8.3.1 Jelinski–Moranda De-eutrophication Model with a Change
Point . 159
8.3.1.1 Model Review . 159
8.3.1.2 Model with One Change Point 159
8.3.2 Weibull Change-point Model 160
8.3.3 Littlewood Model with One Change Point . 160
8.4 Maximum Likelihood Estimation 160
8.5 Application 161
8.6 Summary . 162
9 Concepts and Applications of Stochastic Aging in Reliability
C. D. Lai and M. Xie . 165
9.1 Introduction 165
9.2 Basic Concepts for Univariate Reliability Classes 167
9.2.1 Some Acronyms and the Notions of Aging . 167
9.2.2 Definitions of Reliability Classes 167
9.2.3 Interrelationships 169
9.3 Properties of the Basic Concepts . 169
9.3.1 Properties of Increasing and Decreasing Failure Rates . 169
9.3.2 Property of Increasing Failure Rate on Average . 169
9.3.3 Properties of NBU, NBUC, and NBUE 169
9.4 Distributions with Bathtub-shaped Failure Rates 169
9.5 Life Classes Characterized by the Mean Residual Lifetime . 170
9.6 Some Further Classes of Aging 171
9.7 Partial Ordering of Life Distributions 171
9.7.1 Relative Aging 172
9.7.2 Applications of Partial Orderings 172
9.8 Bivariate Reliability Classes . 173
9.9 Tests of Stochastic Aging . 173
9.9.1 A General Sketch of Tests 174
9.9.2 Summary of Tests of Aging in Univariate Case . 177
9.9.3 Summary of Tests of Bivariate Aging 177
9.10 Concluding Remarks on Aging 177xvi Contents
10 Class of NBU-t0 Life Distribution
Dong Ho Park . 181
10.1 Introduction 181
10.2 Characterization of NBU-t0 Class 182
10.2.1 Boundary Members of NBU-t0 and NWU-t0 182
10.2.2 Preservation of NBU-t0 and NWU-t0 Properties under
Reliability Operations 184
10.3 Estimation of NBU-t0 Life Distribution . 186
10.3.1 Reneau–Samaniego Estimator 186
10.3.2 Chang–Rao Estimator 188
10.3.2.1 Positively Biased Estimator 188
10.3.2.2 Geometric Mean Estimator 188
10.4 Tests for NBU-t0 Life Distribution 189
10.4.1 Tests for NBU-t0 Alternatives Using Complete Data 189
10.4.1.1 Hollander–Park–Proschan Test 190
10.4.1.2 Ebrahimi–Habibullah Test 192
10.4.1.3 Ahmad Test 193
10.4.2 Tests for NBU-t0 Alternatives Using Incomplete Data . 195
PART III. Software Reliability
11 Software Reliability Models: A Selective Survey and New Directions
Siddhartha R. Dalal . 201
11.1 Introduction 201
11.2 Static Models . 203
11.2.1 Phase-based Model: Gaffney and Davis . 203
11.2.2 Predictive Development Life Cycle Model: Dalal and Ho 203
11.3 Dynamic Models: Reliability Growth Models for Testing and
Operational Use 205
11.3.1 A General Class of Models 205
11.3.2 Assumptions Underlying the Reliability Growth Models 206
11.3.3 Caution in Using Reliability Growth Models 207
11.4 Reliability Growth Modeling with Covariates 207
11.5 When to Stop Testing Software 208
11.6 Challenges and Conclusions . 209
12 Software Reliability Modeling
James Ledoux . 213
12.1 Introduction 213
12.2 Basic Concepts of Stochastic Modeling . 214
12.2.1 Metrics with Regard to the First Failure . 214
12.2.2 Stochastic Process of Times of Failure 215
12.3 Black-box Software Reliability Models 215
12.3.1 Self-exciting Point Processes . 216
12.3.1.1 Counting Statistics for a Self-exciting Point Process . 218Contents xvii
12.3.1.2 Likelihood Function for a Self-exciting Point Process 218
12.3.1.3 Reliability and Mean Time to Failure Functions . 218
12.3.2 Classification of Software Reliability Models 219
12.3.2.1 0-Memory Self-exciting Point Process 219
12.3.2.2 Non-homogeneous Poisson Process Model:
?(t; Ht, F0) = f (t; F0) and is Deterministic 220
12.3.2.3 1-Memory Self-exciting Point Process with
?(t; Ht, F0) = f (N(t), t ? TN(t), F0) 221
12.3.2.4 m ? 2-Memory 221
12.4 White-box Modeling . 222
12.5 Calibration of Model . 223
12.5.1 Frequentist Procedures 223
12.5.2 Bayesian Procedure . 225
12.6 Current Issues . 225
12.6.1 Black-box Modeling . 225
12.6.1.1 Imperfect Debugging . 225
12.6.1.2 Early Prediction of Software Reliability . 226
12.6.1.3 Environmental Factors 227
12.6.1.4 Conclusion . 228
12.6.2 White-box Modeling . 229
12.6.3 Statistical Issues . 230
13 Software Availability Theory and Its Applications
Koichi Tokuno and Shigeru Yamada . 235
13.1 Introduction 235
13.2 Basic Model and Software Availability Measures 236
13.3 Modified Models . 239
13.3.1 Model with Two Types of Failure 239
13.3.2 Model with Two Types of Restoration 240
13.4 Applied Models 241
13.4.1 Model with Computation Performance . 241
13.4.2 Model for Hardware–Software System . 242
13.5 Concluding Remarks . 243
14 Software Rejuvenation: Modeling and Applications
Tadashi Dohi, Katerina Go?eva-Popstojanova, Kalyanaraman Vaidyanathan,
Kishor S. Trivedi and Shunji Osaki 245
14.1 Introduction 245
14.2 Modeling-based Estimation . 246
14.2.1 Examples in Telecommunication Billing Applications . 247
14.2.2 Examples in a Transaction-based Software System . 251
14.2.3 Examples in a Cluster System 255
14.3 Measurement-based Estimation . 257
14.3.1 Time-based Estimation . 258
14.3.2 Time and Workload-based Estimation . 260
14.4 Conclusion and Future Work . 262xviii Contents
15 Software Reliability Management: Techniques and Applications
Mitsuhiro Kimura and Shigeru Yamada . 265
15.1 Introduction 265
15.2 Death Process Model for Software Testing Management 266
15.2.1 Model Description 267
15.2.1.1 Mean Number of Remaining Software Faults/Testing
Cases 268
15.2.1.2 Mean Time to Extinction . 268
15.2.2 Estimation Method of Unknown Parameters 268
15.2.2.1 Case of 0 < ? ? 1 . 268
15.2.2.2 Case of ? = 0 . 269
15.2.3 Software Testing Progress Evaluation 269
15.2.4 Numerical Illustrations . 270
15.2.5 Concluding Remarks . 271
15.3 Estimation Method of Imperfect Debugging Probability 271
15.3.1 Hidden-Markov modeling for software reliability growth
phenomenon . 271
15.3.2 Estimation Method of Unknown Parameters 272
15.3.3 Numerical Illustrations . 273
15.3.4 Concluding Remarks . 274
15.4 Continuous State Space Model for Large-scale Software 274
15.4.1 Model Description 275
15.4.2 Nonlinear Characteristics of Software Debugging Speed 277
15.4.3 Estimation Method of Unknown Parameters 277
15.4.4 Software Reliability Assessment Measures . 279
15.4.4.1 Expected Number of Remaining Faults and Its
Variance 279
15.4.4.2 Cumulative and Instantaneous Mean Time Between
Failures 279
15.4.5 Concluding Remarks . 280
15.5 Development of a Software Reliability Management Tool 280
15.5.1 Definition of the Specification Requirement 280
15.5.2 Object-oriented Design . 281
15.5.3 Examples of Reliability Estimation and Discussion 282
16 Recent Studies in Software Reliability Engineering
Hoang Pham . 285
16.1 Introduction 285
16.1.1 Software Reliability Concepts 285
16.1.2 Software Life Cycle 288
16.2 Software Reliability Modeling 288
16.2.1 A Generalized Non-homogeneous Poisson Process Model . 289
16.2.2 Application 1: The Real-time Control System 289
16.3 Generalized Models with Environmental Factors 289
16.3.1 Parameters Estimation 292
16.3.2 Application 2: The Real-time Monitor Systems . 292Contents xix
16.4 Cost Modeling . 295
16.4.1 Generalized Risk–Cost Models . 295
16.5 Recent Studies with Considerations of Random Field Environments . 296
16.5.1 A Reliability Model 297
16.5.2 A Cost Model . 297
16.6 Further Reading 300
PART IV. Maintenance Theory and Testing
17 Warranty and Maintenance
D. N. P. Murthy and N. Jack 305
17.1 Introduction 305
17.2 Product Warranties: An Overview 306
17.2.1 Role and Concept . 306
17.2.2 Product Categories 306
17.2.3 Warranty Policies . 306
17.2.3.1 Warranties Policies for Standard Products Sold
Individually 306
17.2.3.2 Warranty Policies for Standard Products Sold in Lots 307
17.2.3.3 Warranty Policies for Specialized Products . 307
17.2.3.4 Extended Warranties . 307
17.2.3.5 Warranties for Used Products 308
17.2.4 Issues in Product Warranty . 308
17.2.4.1 Warranty Cost Analysis 308
17.2.4.2 Warranty Servicing 309
17.2.5 Review of Warranty Literature 309
17.3 Maintenance: An Overview 309
17.3.1 Corrective Maintenance . 309
17.3.2 Preventive Maintenance . 310
17.3.3 Review of Maintenance Literature 310
17.4 Warranty and Corrective Maintenance . 311
17.5 Warranty and Preventive Maintenance . 312
17.6 Extended Warranties and Service Contracts . 313
17.7 Conclusions and Topics for Future Research 314
18 Mechanical Reliability and Maintenance Models
Gianpaolo Pulcini . 317
18.1 Introduction 317
18.2 Stochastic Point Processes 318
18.3 Perfect Maintenance . 320
18.4 Minimal Repair 321
18.4.1 No Trend with Operating Time . 323
18.4.2 Monotonic Trend with Operating Time . 323
18.4.2.1 The Power Law Process 324
18.4.2.2 The Log–Linear Process 325
18.4.2.3 Bounded Intensity Processes . 326xx Contents
18.4.3 Bathtub-type Intensity 327
18.4.3.1 Numerical Example 328
18.4.4 Non-homogeneous Poisson Process Incorporating Covariate
Information 329
18.5 Imperfect or Worse Repair 330
18.5.1 Proportional Age Reduction Models 330
18.5.2 Inhomogeneous Gamma Processes . 331
18.5.3 Lawless–Thiagarajah Models 333
18.5.4 Proportional Intensity Variation Model . 334
18.6 Complex Maintenance Policy . 335
18.6.1 Sequence of Perfect and Minimal Repairs Without Preventive
Maintenance . 336
18.6.2 Minimal Repairs Interspersed with Perfect Preventive
Maintenance . 338
18.6.3 Imperfect Repairs Interspersed with Perfect Preventive
Maintenance . 339
18.6.4 Minimal Repairs Interspersed with Imperfect Preventive
Maintenance . 340
18.6.4.1 Numerical Example 341
18.6.5 Corrective Repairs Interspersed with Preventive Maintenance
Without Restrictive Assumptions 342
18.7 Reliability Growth . 343
18.7.1 Continuous Models 344
18.7.2 Discrete Models . 345
19 Preventive Maintenance Models: Replacement, Repair, Ordering, and Inspection
Tadashi Dohi, Naoto Kaio and Shunji Osaki . 349
19.1 Introduction 349
19.2 Block Replacement Models 350
19.2.1 Model I 350
19.2.2 Model II 352
19.2.3 Model III . 352
19.3 Age Replacement Models . 354
19.3.1 Basic Age Replacement Model 354
19.4 Ordering Models . 356
19.4.1 Continuous-time Model . 357
19.4.2 Discrete-time Model . 358
19.4.3 Combined Model with Minimal Repairs 359
19.5 Inspection Models 361
19.5.1 Nearly Optimal Inspection Policy by Kaio and Osaki (K&O
Policy) 362
19.5.2 Nearly Optimal Inspection Policy by Munford and Shahani
(M&S Policy) . 363
19.5.3 Nearly Optimal Inspection Policy by Nakagawa and Yasui
(N&Y Policy) . 363
19.6 Concluding Remarks . 363Contents xxi
20 Maintenance and Optimum Policy
Toshio Nakagawa . 367
20.1 Introduction 367
20.2 Replacement Policies . 368
20.2.1 Age Replacement . 368
20.2.2 Block Replacement 370
20.2.2.1 No Replacement at Failure 370
20.2.2.2 Replacement with Two Variables . 371
20.2.3 Periodic Replacement 371
20.2.3.1 Modified Models with Two Variables . 372
20.2.3.2 Replacement at N Variables . 373
20.2.4 Other Replacement Models . 373
20.2.4.1 Replacements with Discounting . 373
20.2.4.2 Discrete Replacement Models 374
20.2.4.3 Replacements with Two Types of Unit 375
20.2.4.4 Replacement of a Shock Model 376
20.2.5 Remarks . 377
20.3 Preventive Maintenance Policies . 378
20.3.1 One-unit System . 378
20.3.1.1 Interval Reliability 379
20.3.2 Two-unit System . 380
20.3.3 Imperfect Preventive Maintenance . 381
20.3.3.1 Imperfect with Probability 383
20.3.3.2 Reduced Age 383
20.3.4 Modified Preventive Maintenance 384
20.4 Inspection Policies 385
20.4.1 Standard Inspection . 386
20.4.2 Inspection with Preventive Maintenance 387
20.4.3 Inspection of a Storage System . 388
21 Optimal Imperfect Maintenance Models
Hongzhou Wang and Hoang Pham 397
21.1 Introduction 397
21.2 Treatment Methods for Imperfect Maintenance . 399
21.2.1 Treatment Method 1 . 399
21.2.2 Treatment Method 2 . 400
21.2.3 Treatment Method 3 . 401
21.2.4 Treatment Method 4 . 402
21.2.5 Treatment Method 5 . 403
21.2.6 Treatment Method 6 . 403
21.2.7 Treatment Method 7 . 403
21.2.8 Other Methods 404
21.3 Some Results on Imperfect Maintenance 404
21.3.1 A Quasi-renewal Process and Imperfect Maintenance . 404
21.3.1.1 Imperfect Maintenance Model A . 405
21.3.1.2 Imperfect Maintenance Model B . 405xxii Contents
21.3.1.3 Imperfect Maintenance Model C . 405
21.3.1.4 Imperfect Maintenance Model D . 407
21.3.1.5 Imperfect Maintenance Model E . 408
21.3.2 Optimal Imperfect Maintenance of k-out-of-n Systems 409
21.4 Future Research on Imperfect Maintenance . 411
21.A Appendix . 412
21.A.1 Acronyms and Definitions 412
21.A.2 Exercises . 412
22 Accelerated Life Testing
Elsayed A. Elsayed 415
22.1 Introduction 415
22.2 Design of Accelerated Life Testing Plans . 416
22.2.1 Stress Loadings 416
22.2.2 Types of Stress 416
22.3 Accelerated Life Testing Models . 417
22.3.1 Parametric Statistics-based Models . 418
22.3.2 Acceleration Model for the Exponential Model . 419
22.3.3 Acceleration Model for the Weibull Model . 420
22.3.4 The Arrhenius Model 422
22.3.5 Non-parametric Accelerated Life Testing Models: Cox’s Model 424
22.4 Extensions of the Proportional Hazards Model . 426
23 Accelerated Test Models with the Birnbaum–Saunders Distribution
W. Jason Owen and William J. Padgett 429
23.1 Introduction 429
23.1.1 Accelerated Testing 430
23.1.2 The Birnbaum–Saunders Distribution . 431
23.2 Accelerated Birnbaum–Saunders Models 431
23.2.1 The Power-law Accelerated Birnbaum–Saunders Model 432
23.2.2 Cumulative Damage Models . 432
23.2.2.1 Additive Damage Models . 433
23.2.2.2 Multiplicative Damage Models 434
23.3 Inference Procedures with Accelerated Life Models . 435
23.4 Estimation from Experimental Data . 437
23.4.1 Fatigue Failure Data . 437
23.4.2 Micro-Composite Strength Data . 437
24 Multiple-steps Step-stress Accelerated Life Test
Loon-Ching Tang . 441
24.1 Introduction 441
24.2 Cumulative Exposure Models 443
24.3 Planning a Step-stress Accelerated Life Test . 445
24.3.1 Planning a Simple Step-stress Accelerated Life Test 446
24.3.1.1 The Likelihood Function . 446
24.3.1.2 Setting a Target Accelerating Factor . 447Contents xxiii
24.3.1.3 Maximum Likelihood Estimator and Asymptotic
Variance 447
24.3.1.4 Nonlinear Programming for Joint Optimality in
Hold Time and Low Stress 447
24.3.2 Multiple-steps Step-stress Accelerated Life Test Plans . 448
24.4 Data Analysis in the Step-stress Accelerated Life Test 450
24.4.1 Multiply Censored, Continuously Monitored Step-stress
Accelerated Life Test . 450
24.4.1.1 Parameter Estimation for Weibull Distribution . 451
24.4.2 Read-out Data 451
24.5 Implementation in Microsoft ExcelTM 453
24.6 Conclusion 454
25 Step-stress Accelerated Life Testing
Chengjie Xiong 457
25.1 Introduction 457
25.2 Step-stress Life Testing with Constant Stress-change Times 457
25.2.1 Cumulative Exposure Model . 457
25.2.2 Estimation with Exponential Data 459
25.2.3 Estimation with Other Distributions 462
25.2.4 Optimum Test Plan 463
25.3 Step-stress Life Testing with Random Stress-change Times 463
25.3.1 Marginal Distribution of Lifetime 463
25.3.2 Estimation 467
25.3.3 Optimum Test Plan 467
25.4 Bibliographical Notes . 468
PART V. Practices and Emerging Applications
26 Statistical Methods for Reliability Data Analysis
Michael J. Phillips . 475
26.1 Introduction 475
26.2 Nature of Reliability Data . 475
26.3 Probability and Random Variables 478
26.4 Principles of Statistical Methods . 479
26.5 Censored Data . 480
26.6 Weibull Regression Model 483
26.7 Accelerated Failure-time Model . 485
26.8 Proportional Hazards Model . 486
26.9 Residual Plots for the Proportional Hazards Model . 489
26.10 Non-proportional Hazards Models . 490
26.11 Selecting the Model and the Variables 491
26.12 Discussion . 491xxiv Contents
27 The Application of Capture–Recapture Methods in Reliability Studies
Paul S. F. Yip, Yan Wang and Anne Chao 493
27.1 Introduction 493
27.2 Formulation of the Problem . 495
27.2.1 Homogeneous Model with Recapture 496
27.2.2 A Seeded Fault Approach Without Recapture 498
27.2.3 Heterogeneous Model 499
27.2.3.1 Non-parametric Case: ?i(t) = ?i?t 499
27.2.3.2 Parametric Case: ?i(t) = ?i 501
27.3 A Sequential Procedure 504
27.4 Real Examples . 504
27.5 Simulation Studies 505
27.6 Discussion . 508
28 Reliability of Electric Power Systems: An Overview
Roy Billinton and Ronald N. Allan 511
28.1 Introduction 511
28.2 System Reliability Performance . 512
28.3 System Reliability Prediction . 515
28.3.1 System Analysis . 515
28.3.2 Predictive Assessment at HLI 516
28.3.3 Predictive Assessment at HLII 518
28.3.4 Distribution System Reliability Assessment . 519
28.3.5 Predictive Assessment at HLIII . 520
28.4 System Reliability Data 521
28.4.1 Canadian Electricity Association Database . 522
28.4.2 Canadian Electricity Association Equipment Reliability
Information System Database for HLI Evaluation . 523
28.4.3 Canadian Electricity Association Equipment Reliability
Information System Database for HLII Evaluation . 523
28.4.4 Canadian Electricity Association Equipment Reliability
Information System Database for HLIII Evaluation 524
28.5 System Reliability Worth . 525
28.6 Guide to Further Study 527
29 Human and Medical Device Reliability
B. S. Dhillon 529
29.1 Introduction 529
29.2 Human and Medical Device Reliability Terms and Definitions . 529
29.3 Human Stress—Performance Effectiveness, Human Error Types, and
Causes of Human Error 530
29.4 Human Reliability Analysis Methods 531
29.4.1 Probability Tree Method . 531
29.4.2 Fault Tree Method 532
29.4.3 Markov Method . 534Contents xxv
29.5 Human Unreliability Data Sources 535
29.6 Medical Device Reliability Related Facts and Figures 535
29.7 Medical Device Recalls and Equipment Classification . 536
29.8 Human Error in Medical Devices 537
29.9 Tools for Medical Device Reliability Assurance . 537
29.9.1 General Method . 538
29.9.2 Failure Modes and Effect Analysis 538
29.9.3 Fault Tree Method 538
29.9.4 Markov Method . 538
29.10 Data Sources for Performing Medical Device Reliability Studies 539
29.11 Guidelines for Reliability Engineers with Respect to Medical Devices . 539
30 Probabilistic Risk Assessment
Robert A. Bari . 543
30.1 Introduction 543
30.2 Historical Comments . 544
30.3 Probabilistic Risk Assessment Methodology 546
30.4 Engineering Risk Versus Environmental Risk 549
30.5 Risk Measures and Public Impact 550
30.6 Transition to Risk-informed Regulation . 553
30.7 Some Successful Probabilistic Risk Assessment Applications 553
30.8 Comments on Uncertainty 554
30.9 Deterministic, Probabilistic, Prescriptive, Performance-based . 554
30.10 Outlook 555
31 Total Dependability Management
Per Anders Akersten and Bengt Klefsj? . 559
31.1 Introduction 559
31.2 Background 559
31.3 Total Dependability Management 560
31.4 Management System Components 561
31.5 Conclusions 564
32 Total Quality for Software Engineering Management
G. Albeanu and Fl. Popentiu Vladicescu . 567
32.1 Introduction 567
32.1.1 The Meaning of Software Quality 567
32.1.2 Approaches in Software Quality Assurance . 569
32.2 The Practice of Software Engineering 571
32.2.1 Software Lifecycle 571
32.2.2 Software Development Process . 574
32.2.3 Software Measurements . 575
32.3 Software Quality Models . 577
32.3.1 Measuring Aspects of Quality 577
32.3.2 Software Reliability Engineering 577
32.3.3 Effort and Cost Models 579xxvi Contents
32.4 Total Quality Management for Software Engineering 580
32.4.1 Deming’s Theory . 580
32.4.2 Continuous Improvement 581
32.5 Conclusions 582
33 Software Fault Tolerance
Xiaolin Teng and Hoang Pham 585
33.1 Introduction 585
33.2 Software Fault-tolerant Methodologies . 586
33.2.1 N-version Programming . 586
33.2.2 Recovery Block 586
33.2.3 Other Fault-tolerance Techniques 587
33.3 N-version Programming Modeling . 588
33.3.1 Basic Analysis 588
33.3.1.1 Data-domain Modeling 588
33.3.1.2 Time-domain Modeling 589
33.3.2 Reliability in the Presence of Failure Correlation 590
33.3.3 Reliability Analysis and Modeling 591
33.4 Generalized Non-homogeneous Poisson Process Model Formulation . 594
33.5 Non-homogeneous Poisson Process Reliability Model for N-version
Programming Systems 595
33.5.1 Model Assumptions . 597
33.5.2 Model Formulations . 599
33.5.2.1 Mean Value Functions . 599
33.5.2.2 Common Failures . 600
33.5.2.3 Concurrent Independent Failures 601
33.5.3 N-version Programming System Reliability 601
33.5.4 Parameter Estimation 602
33.6 N-version programming–Software Reliability Growth . 602
33.6.1 Applications of N-version Programming–Software Reliability
Growth Models 602
33.6.1.1 Testing Data 602
33.7 Conclusion 610
34 Markovian Dependability/Performability Modeling of Fault-tolerant Systems
Juan A. Carrasco . 613
34.1 Introduction 613
34.2 Measures . 615
34.2.1 Expected Steady-state Reward Rate . 617
34.2.2 Expected Cumulative Reward Till Exit of a Subset of States 618
34.2.3 Expected Cumulative Reward During Stay in a Subset of States 618
34.2.4 Expected Transient Reward Rate 619
34.2.5 Expected Averaged Reward Rate . 619
34.2.6 Cumulative Reward Distribution Till Exit of a Subset of States 619
34.2.7 Cumulative Reward Distribution During Stay in a Subset
of States 620Contents xxvii
34.2.8 Cumulative Reward Distribution 621
34.2.9 Extended Reward Structures . 621
34.3 Model Specification 622
34.4 Model Solution 625
34.5 The Largeness Problem 630
34.6 A Case Study . 632
34.7 Conclusions 640
35 Random-request Availability
Kang W. Lee 643
35.1 Introduction 643
35.2 System Description and Definition 644
35.3 Mathematical Expression for the Random-request Availability 645
35.3.1 Notation . 645
35.3.2 Mathematical Assumptions . 645
35.3.3 Mathematical Expressions 645
35.4 Numerical Examples . 647
35.5 Simulation Results 647
35.6 Approximation 651
35.7 Concluding Remarks . 652
Index .


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