Handbook of Reliability Engineering
作者：cad 提交日期：2008-12-2| 分类: | 访问量：
Handbook of Reliability Engineering
本帖被 tdragonfu 执行锁定操作(2007-12-27)
Springer - Handbook of Reliability Engineering.pdf
[ 此贴被tdragonfu在2007-12-27 16:59重新编辑 ]
附件： Springer - Handbook of Reliability Engineering.part1.rar (4102 K) 下载次数:67
全了
附件： Springer - Handbook of Reliability Engineering.part2.rar (3363 K) 下载次数:60
图片：
PART I. System Reliability and Optimization
1 Multi-state k-out-of-n Systems
Ming J. Zuo, Jinsheng Huang andWay Kuo . . . . . . . . . . . . . . . . . . . 3
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Relevant Concepts in Binary Reliability Theory . . . . . . . . . . . . . 3
1.3 Binary k-out-of-nModels . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.1 The k-out-of-n:G System with Independently and Identically
DistributedComponents . . . . . . . . . . . . . . . . . . . . . 5
1.3.2 Reliability Evaluation Using Minimal Path or Cut Sets . . . . . 5
1.3.3 RecursiveAlgorithms . . . . . . . . . . . . . . . . . . . . . . 6
1.3.4 Equivalence Between a k-out-of-n:G System and an
(n − k + 1)-out-of-n:Fsystem . . . . . . . . . . . . . . . . . . 6
1.3.5 The Dual Relationship Between the k-out-of-n G and F Systems 7
1.4 RelevantConceptsinMulti-stateReliabilityTheory . . . . . . . . . . 8
1.5 A Simple Multi-state k-out-of-n:GModel . . . . . . . . . . . . . . . . 10
1.6 A Generalized Multi-state k-out-of-n:GSystemModel . . . . . . . . . 11
1.7 Properties of Generalized Multi-state k-out-of-n:GSystems . . . . . . 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 TheSeriesSystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 TheParallelSystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 CostOptimization . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 TheParallel–SeriesSystem . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.1 TheProfitMaximizationProblem . . . . . . . . . . . . . . . . 23
2.4.2 OptimizationProblem . . . . . . . . . . . . . . . . . . . . . . 24
2.5 TheSeries–ParallelSystem . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5.1 MaximizingtheAverageSystemProfit . . . . . . . . . . . . . 26
2.5.2 ConsiderationofTypeIDesignError . . . . . . . . . . . . . . 27
2.6 The k-out-of-n Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.6.1 Minimizing the Average SystemCost . . . . . . . . . . . . . . 29
2.7 Fault-tolerantSystems . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.7.1 ReliabilityEvaluation . . . . . . . . . . . . . . . . . . . . . . 332.7.2 RedundancyOptimization . . . . . . . . . . . . . . . . . . . . 34
2.8 WeightedSystemswithThreeFailureModes . . . . . . . . . . . . . . 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 ComputationofReliability . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.1 TheRecursiveEquationApproach . . . . . . . . . . . . . . . 39
3.2.2 TheMarkovChainApproach . . . . . . . . . . . . . . . . . . 40
3.2.3 AsymptoticAnalysis . . . . . . . . . . . . . . . . . . . . . . . 41
3.3 InvariantConsecutiveSystems . . . . . . . . . . . . . . . . . . . . . . 41
3.3.1 InvariantConsecutive-2Systems . . . . . . . . . . . . . . . . 41
3.3.2 Invariant Consecutive-k Systems . . . . . . . . . . . . . . . . 42
3.3.3 Invariant Consecutive-kGSystem. . . . . . . . . . . . . . . . 43
3.4 Component Importance and the Component Replacement Problem . 43
3.4.1 TheBirnbaumImportance . . . . . . . . . . . . . . . . . . . . 44
3.4.2 PartialBirnbaumImportance . . . . . . . . . . . . . . . . . . 45
3.4.3 TheOptimalComponentReplacement . . . . . . . . . . . . . 45
3.5 TheWeighted-consecutive-k-out-of-n System. . . . . . . . . . . . . . 47
3.5.1 The LinearWeighted-consecutive-k-out-of-n System . . . . . 47
3.5.2 The CircularWeighted-consecutive-k-out-of-n System . . . . 47
3.6 WindowSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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-windowSystem . . . . . . . . . . . . . . . . . . . 52
3.7 NetworkSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.7.1 The Linear Consecutive-2 Network System . . . . . . . . . . . 53
3.7.2 The Linear Consecutive-kNetworkSystem . . . . . . . . . . . 54
3.7.3 The Linear Consecutive-k FlowNetworkSystem . . . . . . . . 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 SystemReliabilityMeasures . . . . . . . . . . . . . . . . . 63
4.3 Multi-state System Reliability Indices Evaluation Based on the
UniversalGeneratingFunction . . . . . . . . . . . . . . . . . . . . . . 64
4.4 Determination of u-function of ComplexMulti-state System Using
CompositionOperators . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.5 Importance and Sensitivity Analysis of Multi-state Systems . . . . . . 68
4.6 Multi-state SystemStructureOptimizationProblems . . . . . . . . . . 72
4.6.1 OptimizationTechnique . . . . . . . . . . . . . . . . . . . . . 73
4.6.1.1 GeneticAlgorithm . . . . . . . . . . . . . . . . . . 73
4.6.1.2 Solution Representation and Decoding Procedure . 75
4.6.2 Structure Optimization of Series–Parallel System with
Capacity-basedPerformanceMeasure . . . . . . . . . . . . . 75
4.6.2.1 ProblemFormulation . . . . . . . . . . . . . . . . . 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 ProblemFormulation . . . . . . . . . . . . . . . . . 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 ProblemFormulation . . . . . . . . . . . . . . . . . 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
ProducingSubsystem . . . . . . . . . . . . . . . . . 85
4.6.4.4 The Output Performance Distribution of a System
Containing Different Elements in the Main
ProducingSubsystem . . . . . . . . . . . . . . . . . 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 OptimalSolutionApproaches . . . . . . . . . . . . . . . . . . 95
5.2.1.1 Partial Enumeration Method . . . . . . . . . . . . . 95
5.2.1.2 Branch-and-bound Method . . . . . . . . . . . . . . 96
5.2.1.3 DynamicProgramming . . . . . . . . . . . . . . . . 98
5.2.2 HeuristicSolutionApproach . . . . . . . . . . . . . . . . . . 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-choiceConstraints . . . . . . . . . . . . . . . . . . . . . . . 107
5.4.1 One-dimensionalProblems . . . . . . . . . . . . . . . . . . . 108
5.4.2 Multi-dimensionalProblems . . . . . . . . . . . . . . . . . . 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 inthePlane . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.5.1 Examples of Bivariate Positive Dependence Stronger than
PositiveQuadrantDependentCondition . . . . . . . . . . . . 152
7.5.2 ExamplesofNegativeQuadrantDependence . . . . . . . . . . 153
7.6 PositiveDependenceOrderings . . . . . . . . . . . . . . . . . . . . . 153
7.7 ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 SomeSpecificChange-pointModels . . . . . . . . . . . . . . . . . . . 159
8.3.1 Jelinski–Moranda De-eutrophication Model with a Change
Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
8.3.1.1 ModelReview . . . . . . . . . . . . . . . . . . . . . 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 MaximumLikelihoodEstimation . . . . . . . . . . . . . . . . . . . . 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 DefinitionsofReliabilityClasses . . . . . . . . . . . . . . . . 167
9.2.3 Interrelationships . . . . . . . . . . . . . . . . . . . . . . . . 169
9.3 Propertiesof theBasicConcepts . . . . . . . . . . . . . . . . . . . . . 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 DistributionswithBathtub-shapedFailureRates . . . . . . . . . . . . 169
9.5 Life Classes Characterized by the Mean Residual Lifetime . . . . . . . 170
9.6 SomeFurtherClassesofAging . . . . . . . . . . . . . . . . . . . . . . 171
9.7 PartialOrderingofLifeDistributions . . . . . . . . . . . . . . . . . . 171
9.7.1 RelativeAging . . . . . . . . . . . . . . . . . . . . . . . . . . 172
9.7.2 ApplicationsofPartialOrderings . . . . . . . . . . . . . . . . 172
9.8 BivariateReliabilityClasses . . . . . . . . . . . . . . . . . . . . . . . 173
9.9 TestsofStochasticAging . . . . . . . . . . . . . . . . . . . . . . . . . 173
9.9.1 AGeneralSketchofTests . . . . . . . . . . . . . . . . . . . . 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 ConcludingRemarksonAging . . . . . . . . . . . . . . . . . . . . . . 177
10 Class of NBU-t0 Life Distribution
Dong Ho Park . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
10.2 Characterization of NBU-t0Class . . . . . . . . . . . . . . . . . . . . 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
ReliabilityOperations . . . . . . . . . . . . . . . . . . . . . . 184
10.3 Estimation of NBU-t0 LifeDistribution . . . . . . . . . . . . . . . . . 186
10.3.1 Reneau–SamaniegoEstimator . . . . . . . . . . . . . . . . . . 186
10.3.2 Chang–RaoEstimator . . . . . . . . . . . . . . . . . . . . . . 188
10.3.2.1 Positively Biased Estimator . . . . . . . . . . . . . . 188
10.3.2.2 Geometric Mean Estimator . . . . . . . . . . . . . . 188
10.4 Tests for NBU-t0 LifeDistribution . . . . . . . . . . . . . . . . . . . . 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 AhmadTest . . . . . . . . . . . . . . . . . . . . . . 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 StaticModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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
OperationalUse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
11.3.1 AGeneralClassofModels . . . . . . . . . . . . . . . . . . . . 205
11.3.2 Assumptions Underlying the Reliability Growth Models . . . . 206
11.3.3 Caution in Using Reliability Growth Models . . . . . . . . . . 207
11.4 ReliabilityGrowthModelingwithCovariates . . . . . . . . . . . . . . 207
11.5 WhentoStopTestingSoftware . . . . . . . . . . . . . . . . . . . . . . 208
11.6 ChallengesandConclusions . . . . . . . . . . . . . . . . . . . . . . . 209
12 Software Reliability Modeling
James Ledoux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
12.2 BasicConceptsofStochasticModeling . . . . . . . . . . . . . . . . . 214
12.2.1 Metrics with Regard to the First Failure . . . . . . . . . . . . . 214
12.2.2 StochasticProcessofTimesofFailure . . . . . . . . . . . . . . 215
12.3 Black-boxSoftwareReliabilityModels . . . . . . . . . . . . . . . . . . 215
12.3.1 Self-excitingPointProcesses . . . . . . . . . . . . . . . . . . . 216
12.3.1.1 Counting Statistics for a Self-exciting Point Process . 218
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:
λ(t; Ht , F0) = f (t; F0) and is Deterministic . . . . 220
12.3.2.3 1-Memory Self-exciting Point Process with
λ(t; Ht , F0) = f (N(t), t − TN(t), F0) . . . . . . . . 221
12.3.2.4 m ≥ 2-Memory . . . . . . . . . . . . . . . . . . . . 221
12.4 White-boxModeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
12.5 CalibrationofModel . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
12.5.1 FrequentistProcedures . . . . . . . . . . . . . . . . . . . . . . 223
12.5.2 BayesianProcedure . . . . . . . . . . . . . . . . . . . . . . . 225
12.6 Current Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
12.6.1 Black-boxModeling . . . . . . . . . . . . . . . . . . . . . . . 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-boxModeling . . . . . . . . . . . . . . . . . . . . . . . 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 BasicModelandSoftwareAvailabilityMeasures . . . . . . . . . . . . 236
13.3 ModifiedModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
13.3.1 Model with Two Types of Failure . . . . . . . . . . . . . . . . 239
13.3.2 ModelwithTwoTypesofRestoration . . . . . . . . . . . . . . 240
13.4 AppliedModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
13.4.1 ModelwithComputationPerformance . . . . . . . . . . . . . 241
13.4.2 Model for Hardware–Software System . . . . . . . . . . . . . 242
13.5 ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
14 Software Rejuvenation:Modeling and Applications
Tadashi Dohi, Katerina Goševa-Popstojanova, Kalyanaraman Vaidyanathan,
Kishor S. Trivedi and Shunji Osaki . . . . . . . . . . . . . . . . . . . . . . . . 245
14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
14.2 Modeling-basedEstimation . . . . . . . . . . . . . . . . . . . . . . . 246
14.2.1 Examples in Telecommunication Billing Applications . . . . . 247
14.2.2 Examples in a Transaction-based Software System . . . . . . . 251
14.2.3 ExamplesinaClusterSystem . . . . . . . . . . . . . . . . . . 255
14.3 Measurement-basedEstimation . . . . . . . . . . . . . . . . . . . . . 257
14.3.1 Time-basedEstimation . . . . . . . . . . . . . . . . . . . . . 258
14.3.2 Time andWorkload-based Estimation . . . . . . . . . . . . . 260
14.4 ConclusionandFutureWork . . . . . . . . . . . . . . . . . . . . . . . 262
15 Software Reliability Management: Techniques and Applications
Mitsuhiro Kimura and Shigeru Yamada . . . . . . . . . . . . . . . . . . . . . 265
15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
15.2 Death Process Model for Software TestingManagement . . . . . . . . 266
15.2.1 ModelDescription . . . . . . . . . . . . . . . . . . . . . . . . 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 EstimationMethodofUnknownParameters . . . . . . . . . . 268
15.2.2.1 Case of 0<α ≤ 1 . . . . . . . . . . . . . . . . . . . 268
15.2.2.2 Case of α = 0 . . . . . . . . . . . . . . . . . . . . . 269
15.2.3 SoftwareTestingProgressEvaluation . . . . . . . . . . . . . . 269
15.2.4 Numerical Illustrations . . . . . . . . . . . . . . . . . . . . . 270
15.2.5 ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . 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 EstimationMethodofUnknownParameters . . . . . . . . . . 272
15.3.3 Numerical Illustrations . . . . . . . . . . . . . . . . . . . . . 273
15.3.4 ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . 274
15.4 Continuous State Space Model for Large-scale Software . . . . . . . . 274
15.4.1 ModelDescription . . . . . . . . . . . . . . . . . . . . . . . . 275
15.4.2 Nonlinear Characteristics of Software Debugging Speed . . . . 277
15.4.3 EstimationMethodofUnknownParameters . . . . . . . . . . 277
15.4.4 Software Reliability AssessmentMeasures . . . . . . . . . . . 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 ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . 280
15.5 DevelopmentofaSoftwareReliabilityManagementTool . . . . . . . . 280
15.5.1 Definitionof theSpecificationRequirement . . . . . . . . . . 280
15.5.2 Object-orientedDesign . . . . . . . . . . . . . . . . . . . . . 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 SoftwareReliabilityConcepts . . . . . . . . . . . . . . . . . . 285
16.1.2 SoftwareLifeCycle . . . . . . . . . . . . . . . . . . . . . . . . 288
16.2 SoftwareReliabilityModeling . . . . . . . . . . . . . . . . . . . . . . 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 ParametersEstimation . . . . . . . . . . . . . . . . . . . . . . 292
16.3.2 Application 2: The Real-time Monitor Systems . . . . . . . . . 292
16.4 CostModeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
16.4.1 Generalized Risk–CostModels . . . . . . . . . . . . . . . . . 295
16.5 Recent Studies with Considerations of Random Field Environments . 296
16.5.1 AReliabilityModel . . . . . . . . . . . . . . . . . . . . . . . . 297
16.5.2 ACostModel . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
16.6 FurtherReading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 ProductWarranties:AnOverview . . . . . . . . . . . . . . . . . . . . 306
17.2.1 RoleandConcept . . . . . . . . . . . . . . . . . . . . . . . . . 306
17.2.2 ProductCategories . . . . . . . . . . . . . . . . . . . . . . . . 306
17.2.3 WarrantyPolicies . . . . . . . . . . . . . . . . . . . . . . . . . 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 ExtendedWarranties . . . . . . . . . . . . . . . . . 307
17.2.3.5 Warranties for Used Products . . . . . . . . . . . . 308
17.2.4 IssuesinProductWarranty . . . . . . . . . . . . . . . . . . . 308
17.2.4.1 Warranty Cost Analysis . . . . . . . . . . . . . . . . 308
17.2.4.2 WarrantyServicing . . . . . . . . . . . . . . . . . . 309
17.2.5 ReviewofWarrantyLiterature . . . . . . . . . . . . . . . . . . 309
17.3 Maintenance:AnOverview . . . . . . . . . . . . . . . . . . . . . . . . 309
17.3.1 CorrectiveMaintenance . . . . . . . . . . . . . . . . . . . . . 309
17.3.2 PreventiveMaintenance . . . . . . . . . . . . . . . . . . . . . 310
17.3.3 ReviewofMaintenanceLiterature . . . . . . . . . . . . . . . . 310
17.4 WarrantyandCorrectiveMaintenance . . . . . . . . . . . . . . . . . 311
17.5 WarrantyandPreventiveMaintenance . . . . . . . . . . . . . . . . . 312
17.6 ExtendedWarrantiesandServiceContracts . . . . . . . . . . . . . . . 313
17.7 ConclusionsandTopicsforFutureResearch . . . . . . . . . . . . . . 314
18 Mechanical Reliability and MaintenanceModels
Gianpaolo Pulcini . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
18.2 StochasticPointProcesses . . . . . . . . . . . . . . . . . . . . . . . . 318
18.3 PerfectMaintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
18.4 MinimalRepair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
18.4.1 NoTrendwithOperatingTime . . . . . . . . . . . . . . . . . 323
18.4.2 Monotonic Trend with Operating Time . . . . . . . . . . . . . 323
18.4.2.1 ThePowerLawProcess . . . . . . . . . . . . . . . . 324
18.4.2.2 TheLog–LinearProcess . . . . . . . . . . . . . . . . 325
18.4.2.3 Bounded Intensity Processes . . . . . . . . . . . . . 326
20 Maintenance and Optimum Policy
Toshio Nakagawa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
20.2 ReplacementPolicies . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
20.2.1 AgeReplacement . . . . . . . . . . . . . . . . . . . . . . . . . 368
20.2.2 BlockReplacement . . . . . . . . . . . . . . . . . . . . . . . . 370
20.2.2.1 No Replacement at Failure . . . . . . . . . . . . . . 370
20.2.2.2 Replacement with Two Variables . . . . . . . . . . . 371
20.2.3 PeriodicReplacement . . . . . . . . . . . . . . . . . . . . . . 371
20.2.3.1 Modified Models with Two Variables . . . . . . . . . 372
20.2.3.2 Replacement at N Variables . . . . . . . . . . . . . 373
20.2.4 Other ReplacementModels . . . . . . . . . . . . . . . . . . . 373
20.2.4.1 ReplacementswithDiscounting . . . . . . . . . . . 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 PreventiveMaintenancePolicies . . . . . . . . . . . . . . . . . . . . . 378
20.3.1 One-unitSystem . . . . . . . . . . . . . . . . . . . . . . . . . 378
20.3.1.1 IntervalReliability . . . . . . . . . . . . . . . . . . 379
20.3.2 Two-unitSystem . . . . . . . . . . . . . . . . . . . . . . . . . 380
20.3.3 ImperfectPreventiveMaintenance . . . . . . . . . . . . . . . 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 InspectionPolicies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
20.4.1 StandardInspection . . . . . . . . . . . . . . . . . . . . . . . 386
20.4.2 InspectionwithPreventiveMaintenance . . . . . . . . . . . . 387
20.4.3 Inspection of a Storage System . . . . . . . . . . . . . . . . . 388
21 Optimal Imperfect MaintenanceModels
HongzhouWang and Hoang Pham . . . . . . . . . . . . . . . . . . . . . . . . 397
21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
21.2 Treatment Methods for Imperfect Maintenance . . . . . . . . . . . . . 399
21.2.1 TreatmentMethod1 . . . . . . . . . . . . . . . . . . . . . . . 399
21.2.2 TreatmentMethod2 . . . . . . . . . . . . . . . . . . . . . . . 400
21.2.3 TreatmentMethod3 . . . . . . . . . . . . . . . . . . . . . . . 401
21.2.4 TreatmentMethod4 . . . . . . . . . . . . . . . . . . . . . . . 402
21.2.5 TreatmentMethod5 . . . . . . . . . . . . . . . . . . . . . . . 403
21.2.6 TreatmentMethod6 . . . . . . . . . . . . . . . . . . . . . . . 403
21.2.7 TreatmentMethod7 . . . . . . . . . . . . . . . . . . . . . . . 403
21.2.8 OtherMethods . . . . . . . . . . . . . . . . . . . . . . . . . . 404
21.3 SomeResultsonImperfectMaintenance . . . . . . . . . . . . . . . . 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 . . . . . . . . . . . 405
21.3.1.3 Imperfect Maintenance Model C . . . . . . . . . . . 405
21.3.1.4 ImperfectMaintenanceModelD . . . . . . . . . . . 407
21.3.1.5 ImperfectMaintenanceModelE . . . . . . . . . . . 408
21.3.2 Optimal Imperfect Maintenance of k-out-of-n Systems . . . . 409
21.4 FutureResearchonImperfectMaintenance . . . . . . . . . . . . . . . 411
21.A Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
21.A.1 AcronymsandDefinitions . . . . . . . . . . . . . . . . . . . . 412
21.A.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
22 Accelerated Life Testing
Elsayed A. Elsayed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
22.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
22.2 DesignofAcceleratedLifeTestingPlans . . . . . . . . . . . . . . . . . 416
22.2.1 StressLoadings . . . . . . . . . . . . . . . . . . . . . . . . . . 416
22.2.2 TypesofStress . . . . . . . . . . . . . . . . . . . . . . . . . . 416
22.3 AcceleratedLifeTestingModels . . . . . . . . . . . . . . . . . . . . . 417
22.3.1 ParametricStatistics-basedModels . . . . . . . . . . . . . . . 418
22.3.2 AccelerationModel for theExponentialModel . . . . . . . . . 419
22.3.3 Acceleration Model for theWeibull Model . . . . . . . . . . . 420
22.3.4 TheArrheniusModel . . . . . . . . . . . . . . . . . . . . . . 422
22.3.5 Non-parametric Accelerated Life TestingModels: Cox’s Model 424
22.4 Extensionsof theProportionalHazardsModel . . . . . . . . . . . . . 426
23 Accelerated TestModels with the Birnbaum–Saunders Distribution
W. Jason Owen andWilliam J. Padgett . . . . . . . . . . . . . . . . . . . . . . 429
23.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
23.1.1 AcceleratedTesting . . . . . . . . . . . . . . . . . . . . . . . . 430
23.1.2 TheBirnbaum–SaundersDistribution . . . . . . . . . . . . . 431
23.2 AcceleratedBirnbaum–SaundersModels . . . . . . . . . . . . . . . . 431
23.2.1 The Power-law Accelerated Birnbaum–Saunders Model . . . . 432
23.2.2 CumulativeDamageModels . . . . . . . . . . . . . . . . . . . 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 EstimationfromExperimentalData . . . . . . . . . . . . . . . . . . . 437
23.4.1 FatigueFailureData . . . . . . . . . . . . . . . . . . . . . . . 437
23.4.2 Micro-CompositeStrengthData . . . . . . . . . . . . . . . . . 437
24 Multiple-steps Step-stress Accelerated Life Test
Loon-Ching Tang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
24.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
24.2 CumulativeExposureModels . . . . . . . . . . . . . . . . . . . . . . 443
24.3 PlanningaStep-stressAcceleratedLifeTest . . . . . . . . . . . . . . . 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 . . . . . . . . . 447
24.3.1.3 Maximum Likelihood Estimator and Asymptotic
Variance . . . . . . . . . . . . . . . . . . . . . . . . 447
24.3.1.4 Nonlinear Programming for Joint Optimality in
HoldTimeandLowStress . . . . . . . . . . . . . . 447
24.3.2 Multiple-steps Step-stress Accelerated Life Test Plans . . . . . 448
24.4 DataAnalysisintheStep-stressAcceleratedLifeTest . . . . . . . . . . 450
24.4.1 Multiply Censored, Continuously Monitored Step-stress
AcceleratedLifeTest . . . . . . . . . . . . . . . . . . . . . . . 450
24.4.1.1 Parameter Estimation forWeibull Distribution . . . 451
24.4.2 Read-outData . . . . . . . . . . . . . . . . . . . . . . . . . . 451
24.5 Implementation inMicrosoft 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 CumulativeExposureModel . . . . . . . . . . . . . . . . . . . 457
25.2.2 EstimationwithExponentialData . . . . . . . . . . . . . . . . 459
25.2.3 EstimationwithOtherDistributions . . . . . . . . . . . . . . 462
25.2.4 OptimumTestPlan . . . . . . . . . . . . . . . . . . . . . . . . 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 OptimumTestPlan . . . . . . . . . . . . . . . . . . . . . . . . 467
25.4 BibliographicalNotes . . . . . . . . . . . . . . . . . . . . . . . . . . . 468
PART V. Practices and Emerging Applications
26 Statistical Methods for Reliability Data Analysis
Michael J. Phillips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
26.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
26.2 NatureofReliabilityData . . . . . . . . . . . . . . . . . . . . . . . . . 475
26.3 Probability andRandomVariables . . . . . . . . . . . . . . . . . . . . 478
26.4 PrinciplesofStatisticalMethods . . . . . . . . . . . . . . . . . . . . . 479
26.5 CensoredData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
26.6 WeibullRegressionModel . . . . . . . . . . . . . . . . . . . . . . . . 483
26.7 AcceleratedFailure-timeModel . . . . . . . . . . . . . . . . . . . . . 485
26.8 ProportionalHazardsModel . . . . . . . . . . . . . . . . . . . . . . . 486
26.9 ResidualPlots for theProportionalHazardsModel . . . . . . . . . . . 489
26.10 Non-proportionalHazardsModels . . . . . . . . . . . . . . . . . . . 490
26.11 SelectingtheModelandtheVariables . . . . . . . . . . . . . . . . . . 491
26.12 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
本文摘自：http://www.jxcad.com.cn/read.php?tid=493945
问题没解决?请到"CAD家园"查找或求助!
