Modern Statistical And Mathematical Methods In Reliability

By: Sallie Keller-mcnulty (Editor), Alyson Wilson (Editor), Yvonne M Armijo (Editor), Nikolaos Limnios (Editor)

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Hardcover | 4 October 2005

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428 Pages

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This volume contains extended versions of 28 carefully selected and reviewed papers presented at The Fourth International Conference on Mathematical Methods in Reliability in Santa Fe, New Mexico, June 21-25, 2004, the leading conference in reliability research. The meeting serves as a forum for discussing fundamental issues on mathematical methods in reliability theory and its applications.A broad overview of current research activities in reliability theory and its applications is provided with coverage on reliability modeling, network and system reliability, Bayesian methods, survival analysis, degradation and maintenance modeling, and software reliability. The contributors are all leading experts in the field and include the plenary session speakers, Tim Bedford, Thierry Duchesne, Henry Wynn, Vicki Bier, Edsel Pena, Michael Hamada, and Todd Graves.

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Preface	p. v
Competing Risk Modeling in Reliability	p. 1
Introduction	p. 1
Independent and Dependent Competing Risks	p. 3
Characterization of Possible Marginals	p. 5
Kolmogorov-Smirnov Test	p. 7
Conservatism of Independence	p. 8
The Bias of Independence	p. 9
Maintenance as a Censoring Mechanism	p. 10
Dependent copula model	p. 11
Random clipping	p. 11
Random signs	p. 12
LBL model	p. 12
Mixed exponential model	p. 13
Delay time model	p. 13
Loosening the Renewal Assumption	p. 13
Conclusion	p. 15
References	p. 15
Game-Theoretic and Reliability Methods in Counter-Terrorism and Security	p. 17
Introduction	p. 17
Applications of Reliability Analysis to Security	p. 18
Applications of Game Theory to Security	p. 19
Security as a game between defenders	p. 21
Combining Reliability Analysis and Game Theory	p. 23
Directions for Future Work	p. 24
Conclusion	p. 25
Acknowledgments	p. 25
References	p. 26
Regression Models for Reliability Given the Usage Accumulation History	p. 29
Introduction	p. 29
Definitions and notation	p. 30
Common lifetime regression models	p. 31
Other Approaches to Regression Model Building	p. 32
Models based on transfer functionals	p. 33
Models based on internal wear	p. 34
Collapsible Models	p. 36
Two-dimensional prediction problems	p. 36
Discussion	p. 38
Acknowledgments	p. 38
References	p. 38
Bayesian Methods for Assessing System Reliability: Models and Computation	p. 41
Challenges in Modern Reliability Analyses	p. 42
Three Important Examples	p. 42
Example 1: Reliability of a component based on biased sampling	p. 43
Example 2: System reliability based on partially informative tests	p. 44
Example 3: Integrated system reliability based on diverse data	p. 45
YADAS: a Statistical Modeling Environment	p. 46
Expressing arbitrary models	p. 46
Special algorithms	p. 48
Interfaces, present and future	p. 48
Examples Revisited	p. 49
Example 1	p. 49
Example 2	p. 49
Example 3	p. 50
Discussion	p. 51
References	p. 54
Dynamic Modeling in Reliability and Survival Analysis	p. 55
Introduction	p. 55
Dynamic Models	p. 59
A dynamic reliability model	p. 60
A dynamic recurrent event model	p. 61
Some Probabilistic Properties	p. 63
Inference Methods	p. 64
Dynamic load-sharing model	p. 64
Dynamic recurrent event model	p. 65
An Application	p. 68
References	p. 70
End of Life Analysis	p. 73
The Urgency of WEEE	p. 74
The effect on reliability	p. 74
The implications for design	p. 75
Signature Analysis and Hierarchical Modeling	p. 75
The importance of function	p. 76
Wavelets and feature extraction	p. 76
A Case Study	p. 76
Function: preliminary FMEA and life tests	p. 77
Stapler motor: time domain	p. 77
Lifting motor: frequency domain	p. 78
The Development of Protocols and Inversion	p. 79
Acknowledgments	p. 86
References	p. 86
Reliability Analysis of a Dynamic Phased Mission System: Comparison of Two Approaches	p. 87
Introduction	p. 87
Test Case Definition	p. 91
Test Case Resolution	p. 93
Resolution with a Petri net	p. 93
Resolution with a BDMP	p. 96
Compared results	p. 97
Conclusions	p. 100
References	p. 103
Sensitivity Analysis of Accelerated Life Tests with Competing Failure Modes	p. 105
Introduction	p. 106
ALT and Competing Risks	p. 107
ALT and independent competing risks	p. 107
ALT and dependent competing risks	p. 109
Graphical Analysis of Motorettes Data	p. 110
A Copula Dependent ALT - Competing Risk Model	p. 112
Competing risks and copula	p. 112
Measures of association	p. 113
Archimedean copula	p. 114
Application on motor insulation data	p. 114
Conclusions	p. 116
References	p. 117
Estimating Mean Cumulative Functions From Truncated Automotive Warranty Data	p. 121
Introduction	p. 121
The Hu and Lawless Model	p. 123
Extensions of the Model	p. 124
"Time" is age case	p. 124
"Time" is miles case	p. 127
Example	p. 130
The "P-claims" dataset	p. 130
Examples for the "time" is age case	p. 131
Examples for the "time" is miles case	p. 133
Discussion	p. 133
References	p. 134
Tests for Some Statistical Hypotheses for Dependent Competing Risks-A Review	p. 137
Introduction	p. 137
Locally Most Powerful Rank Tests	p. 139
Tests for Bivariate Symmetry	p. 140
Censored Data	p. 144
Simulation Results	p. 145
Test for Independence of T and [delta]	p. 147
Testing H[subscript 0] against H'[subscript 1]	p. 148
Testing H[subscript 0] against H'[subscript 2]	p. 149
Testing H[subscript 0] against H'[subscript 3]	p. 150
Acknowledgments	p. 151
References	p. 151
Repair Efficiency Estimation in the ARI[subscript 1] Imperfect Repair Model	p. 153
Introduction	p. 153
Arithmetic Reduction of Intensity Model with Memory 1	p. 154
Counting process theory	p. 154
Imperfect repair models	p. 155
Failure Process Behavior	p. 156
Minimal and maximal wear intensities	p. 156
Asymptotic intensity	p. 157
Second order term of the asymptotic expanding	p. 159
Repair Efficiency Estimation	p. 160
Maximum likelihood estimators	p. 161
Explicit estimators	p. 163
Empirical Results	p. 164
Finite number of observed failures	p. 164
Application to real maintenance data set and perspective	p. 165
Classical Convergence Theorems	p. 166
References	p. 167
On Repairable Components with Continuous Output	p. 169
Introduction	p. 169
Asymptotic Performance of Repairable Components	p. 171
Simple Systems	p. 173
Imperfect Repair	p. 174
Concluding Remarks	p. 175
References	p. 176
Effects of Uncertainties in Components on the Survival of Complex Systems with Given Dependencies	p. 177
Introduction	p. 177
System Reliability with Dependent Components	p. 179
Bounds on the Margins	p. 181
Uniform metric	p. 182
Quantiles	p. 183
Expectation	p. 184
Bayesian Approach	p. 186
Comparisons	p. 188
References	p. 188
Dynamic Management of Systems Undergoing Evolutionary Acquisition	p. 191
Setting	p. 192
Preamble: broad issues	p. 192
Testing	p. 194
Modeling an Evolutionary Step	p. 195
Model for development of Block b + 1	p. 195
Introduction of design defects during development and testing	p. 196
Examples of mission success probabilities with random K[subscript 0]	p. 197
Acquisition of Block b + 1	p. 198
Obsolescence of Block b and Block b + 1	p. 199
The Decision Problem	p. 199
Examples	p. 200
Conclusion and Future Program	p. 203
References	p. 204
Reliability Analysis of Renewable Redundant Systems with Unreliable Monitoring and Switching	p. 205
Introduction	p. 205
Problem Statement	p. 206
Asymptotic Approach. General System Model	p. 207
Refined System Model and the FS Criterion	p. 207
Estimates of Reliability and Maintainability Indexes	p. 209
Examples	p. 210
Heuristic Approach. Approximate Method of Analysis of Renewal Duplicate System	p. 214
References	p. 218
Planning Models for Component-Based Software Offerings Under Uncertain Operational Profiles	p. 221
Introduction	p. 221
Mathematical Formulation as an Optimal Planning Problem	p. 223
Stochastic Optimal Reliability Allocation	p. 224
Derivation of the distribution for G[subscript 0]	p. 226
Solution implementation	p. 228
Examples	p. 228
Summary and Discussion	p. 230
Acknowledgments	p. 232
References	p. 233
Destructive Stockpile Reliability Assessments: A Semiparametric Estimation of Errors in Variables with Validation Sample Approach	p. 235
Introduction	p. 235
Preliminaries	p. 237
Estimation	p. 238
Proofs	p. 240
Regularity conditions	p. 240
Proof of Theorem 17.2	p. 241
Acknowledgments	p. 244
References	p. 244
Flowgraph Models for Complex Multistate System Reliability	p. 247
Introduction	p. 247
Background on Flowgraph Models	p. 250
Flowgraph Data Analysis	p. 255
Numerical Example	p. 257
Conclusion	p. 260
References	p. 261
Interpretation of Condition Monitoring Data	p. 263
Introduction	p. 263
The Proportional Hazards Model	p. 265
Managing Risk: A CBM Optimization Tool	p. 270
Case Study Papers	p. 272
Food processing: use of vibration monitoring	p. 272
Coal mining: use of oil analysis	p. 273
Nuclear generating station	p. 274
Gearbox subject to tooth failure	p. 276
Future Research Plans	p. 277
References	p. 277
Nonproportional Semiparametric Regression Models for Censored Data	p. 279
Introduction	p. 279
Models and Estimation	p. 280
Accelerated failure time model	p. 280
Rank-based approach	p. 281
Least-squares approach	p. 284
Linear transformation models	p. 286
Remark	p. 289
Acknowledgments	p. 290
References	p. 290
Binary Representations of Multi-State Systems	p. 293
Introduction	p. 293
Basic Definitions	p. 294
Binary Representation of an MSS and Its Properties	p. 296
Examples of Application	p. 301
Conclusions	p. 305
Acknowledgments	p. 306
References	p. 306
Distribution-Free Continuous Bayesian Belief Nets	p. 309
Introduction	p. 309
Vines and Copulae	p. 311
Continuous bbns	p. 315
Example: Flight Crew Alertness Model	p. 318
Conclusions	p. 321
References	p. 321
Statistical Modeling and Inference for Component Failure Times Under Preventive Maintenance and Independent Censoring	p. 323
Introduction	p. 323
Notation, Definitions, and Basic Facts	p. 325
The Repair Alert Model	p. 326
Statistical Inference in the Repair Alert Model	p. 328
Independent censoring	p. 328
Datasets and preliminary graphical model checking	p. 329
Nonparametric estimation	p. 331
Parametric estimation	p. 332
Concluding Remarks	p. 335
References	p. 337
Importance Sampling for Dynamic Systems	p. 339
Introduction	p. 340
Problem Formulation. Reliability and Failure Probability	p. 341
Numerical Examples	p. 343
Linear oscillator excited by white noise	p. 343
Linear oscillator excited by colored noise	p. 348
Conclusions	p. 350
Acknowledgments	p. 351
References	p. 351
Leveraging Remote Diagnostics Data for Predictive Maintenance	p. 353
Introduction	p. 353
Accounting for the Accumulation of Wear	p. 354
Application to Inventory Management of Turbine Blades	p. 356
Developing an Optimal Solution	p. 357
Application	p. 360
Formulating a Generalized Life Regression Model	p. 361
Concluding Remarks	p. 362
Acknowledgments	p. 362
References	p. 362
From Artificial Intelligence to Dependability: Modeling and Analysis with Bayesian Networks	p. 365
Introduction	p. 366
Bayesian Networks	p. 366
Mapping Fault Trees to Bayesian Networks	p. 367
Case Studies: The Digicon Gas Turbine Controller	p. 368
Modeling Issues	p. 371
Probabilistic gates: common cause failures	p. 372
Probabilistic gates: coverage	p. 372
Multi-state variables	p. 373
Sequentially dependent failures	p. 374
Analysis Issues	p. 375
Analysis example	p. 376
Modeling parameter uncertainty in BN model	p. 378
Conclusions and Current Research	p. 380
References	p. 380
Reliability Computation for Usage-Based Testing	p. 383
Motivation	p. 383
Characterizing Use	p. 384
Computing Reliability	p. 387
Models	p. 387
Arc reliabilities	p. 388
Trajectory failure rate	p. 389
Similarity to Expected Use	p. 390
Conclusion	p. 392
References	p. 392
K-Mart Stochastic Modeling Using Iterated Total Time on Test Transforms	p. 395
Introduction	p. 395
Generalized Convexity, Iterated TTT, K-Mart	p. 397
Mixture Models	p. 400
A Binomial Example	p. 403
Construction of "Most Identical" Distribution	p. 407
References	p. 409
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Modern Statistical And Mathematical Methods In Reliability

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