Statistical Models and Methods for Reliability and Survival Analysis

Statistical Models and Methods for Reliability and Survival Analysis brings together contributions by specialists in statistical theory as they discuss their applications providing up-to-date developments in methods used in survival analysis, statistical goodness of fit, stochastic processes for system reliability, amongst others. Many of these are related to the work of Professor M. Nikulin in statistics over the past 30 years. The authors gather together various contributions with a broad array of techniques and results, divided into three parts - Statistical Models and Methods, Statistical Models and Methods in Survival Analysis, and Reliability and Maintenance. The book is intended for researchers interested in statistical methodology and models useful in survival analysis, system reliability and statistical testing for censored and non-censored data.

Table of Contents:
Preface xv Biography of Mikhail Stepanovitch Nikouline xvii Vincent COUALLIER, Léo GERVILLE-RÉACHE, Catherine HUBER-CAROL, Nikolaos LIMNIOS and Mounir MESBAH PART 1. STATISTICAL MODELS AND METHODS  1 Chapter 1. Unidimensionality, Agreement and Concordance Probability 3 Zhezhen JIN and Mounir MESBAH 1.1. Introduction 3 1.2. From reliability to unidimensionality: CAC and curve 4 1.3. Agreement between binary outcomes: the kappa coefficient 10 1.4. Concordance probability 11 1.5. Estimation and inference 14 1.6. Measure of agreement 14 1.7. Extension to survival data 15 1.8. Discussion 17 1.9. Bibliography 18 Chapter 2. A Universal Goodness-of-Fit Test Based on Regression Techniques  21 Florence GEORGE and Sneh GULATI 2.1. Introduction 21 2.2. The Brain and Shapiro procedure for the exponential distribution 22 2.3. Applications of the Brain and Shapiro test 24 2.4. Small sample null distribution of the test statistic for specific distributions 25 2.5. Power studies 28 2.6. Some real examples 28 2.7. Conclusions 31 2.8. Acknowledgment 32 2.9. Bibliography 32 Chapter 3. Entropy-type Goodness-of-Fit Tests for Heavy-Tailed Distributions  33 Andreas MAKRIDES, Alex KARAGRIGORIOU and Filia VONTA 3.1. Introduction 33 3.2. The entropy test for heavy-tailed distributions 35 3.3. Simulation study 40 3.4. Conclusions 42 3.5. Bibliography 42 Chapter 4. Penalized Likelihood Methodology and Frailty Models 45 Emmanouil ANDROULAKIS, Christos KOUKOUVINOS and Filia VONTA 4.1. Introduction 45 4.2. Penalized likelihood in frailty models for clustered data 48 4.3. Simulation results 55 4.4. Concluding remarks 57 4.5. Bibliography 57 Chapter 5. Interactive Investigation of Statistical Regularities in Testing Composite Hypotheses of Goodness of Fit 61 Boris LEMESHKO, Stanislav LEMESHKO and Andrey ROGOZHNIKOV 5.1. Introduction 61 5.2. Distributions of the test statistics in the case of testing composite hypotheses 63 5.3. Testing composite hypotheses in “real-time” 68 5.4. Conclusions 73 5.5. Acknowledgment 73 5.6. Bibliography 73 Chapter 6. Modeling of Categorical Data 77 Henning LÄUTER 6.1. Introduction 77 6.2. Continuous conditional distributions 78 6.3. Discrete conditional distributions 84 6.4. Goodness of fit 86 6.5. Modeling of categorical data 88 6.6. Bibliography 93 Chapter 7. Within the Sample Comparison of Prediction Performance of Models and Submodels: Application to Alzheimer’s Disease 95 Catherine HUBER-CAROL, Shulamith T. GROSS and Annick ALPÉROVITCH 7.1. Introduction 95 7.2. Framework 96 7.3. Estimation of IDI and BRI 97 7.4. Simulation studies 102 7.5. The three city study of Alzheimer’s disease 106 7.6. Conclusion 108 7.7. Bibliography 109 Chapter 8. Durbin–Knott Components and Transformations of the Cramér-von Mises Test  111 Gennady MARTYNOV 8.1. Introduction 111 8.2. Weighted Cramér-von Mises statistic 111 8.3. Examples of the Cramér-von Mises statistics 113 8.4. Weighted parametric Cramér-von Mises statistic 114 8.5. Transformations of the Cramér-von Mises statistic 117 8.6. Bibliography 122 Chapter 9. Conditional Inference in Parametric Models 125 Michel BRONIATOWSKI and Virgile CARON 9.1. Introduction and context 125 9.2. The approximate conditional density of the sample 127 9.3. Sufficient statistics and approximated conditional density 131 9.4. Exponential models with nuisance parameters 135 9.5. Bibliography 142 Chapter 10. On Testing Stochastic Dominance by Exceedance, Precedence and Other Distribution-Free Tests, with Applications 145 Paul DEHEUVELS 10.1. Introduction 145 10.2. Results 148 10.3. Negative binomial limit laws 155 10.4. Conclusion 159 10.5. Bibliography 159 Chapter 11. Asymptotically Parameter-Free Tests for Ergodic Diffusion Processes 161 Yury A. KUTOYANTS and Li ZHOU 11.1. Introduction 161 11.2. Ergodic diffusion process and some limits 165 11.3. Shift parameter 168 11.4. Shift and scale parameters 172 11.5. Bibliography 175 Chapter 12. A Comparison of Homogeneity Tests for Different Alternative Hypotheses 177 Sergey POSTOVALOV and Petr PHILONENKO 12.1. Homogeneity tests 178 12.2. Alternative hypotheses 184 12.3. Power simulation 185 12.4. Statistical inference 191 12.5. Acknowledgment 192 12.6. Bibliography 193 Chapter 13. Some Asymptotic Results for Exchangeably Weighted Bootstraps of the Empirical Estimator of a Semi-Markov Kernel with Applications 195 Salim BOUZEBDA and Nikolaos LIMNIOS 13.1. Introduction 195 13.2. Semi-Markov setting 197 13.3. Main results 201 13.4. Bootstrap for a multidimensional empirical estimator of a continuoustime semi-Markov kernel 205 13.5. Confidence intervals 208 13.6. Bibliography 210 Chapter 14. On Chi-Squared Goodness-of-Fit Test for Normality 213 Mikhail NIKULIN, Léo GERVILLE-RÉACHE and Xuan Quang TRAN 14.1. Chi–squared test for normality 213 14.2. Simulation study 221 14.3. Bibliography 226 PART 2. STATISTICAL MODELS AND METHODS IN SURVIVAL ANALYSIS  229 Chapter 15. Estimation/Imputation Strategies for Missing Data in Survival Analysis 231 Elodie BRUNEL, Fabienne COMTE and Agathe GUILLOUX 15.1. Introduction 231 15.2. Model and strategies 233 15.3. Imputation-based strategy 241 15.4. Numerical comparison 242 15.5. Proofs 244 15.6. Bibliography 251 Chapter 16. Non-Parametric Estimation of Linear Functionals of a Multivariate Distribution Under Multivariate Censoring with Applications 253 Olivier LOPEZ and Philippe SAINT-PIERRE 16.1. Introduction 253 16.2. Non-parametric estimation of the distribution 255 16.3. Asymptotic properties 257 16.4. Statistical applications of functionals 260 16.5. Illustration 263 16.6. Conclusion 264 16.7. Acknowledgment 264 16.8. Bibliography 264 Chapter 17. Kernel Estimation of Density from Indirect Observation 267 Valentin SOLEV 17.1. Introduction 267 17.2. Density of random vector Λ(X) 271 17.3. Pseudo-kernel density estimator 273 17.4. Bibliography 279 Chapter 18. A Comparative Analysis of Some Chi-Square Goodness-of-Fit Tests for Censored Data 281 Ekaterina CHIMITOVA and Boris LEMESHKO 18.1. Introduction 281 18.2. Chi-square goodness-of-fit tests for censored data 283 18.3. The choice of grouping intervals 285 18.4. Empirical power study 290 18.5. Conclusions 293 18.6. Acknowledgment 294 18.7. Bibliography 294 Chapter 19. A Non-parametric Test for Comparing Treatments with Missing Data and Dependent Censoring 297 Amel MEZAOUER, Kamal BOUKHETALA and Jean-François DUPUY 19.1. Introduction 297 19.2. The proposed test statistic 299 19.3. Asymptotic distribution of the proposed test statistic 301 19.4. Acknowledgment 305 19.5. Appendix 306 19.6. Bibliography 309 Chapter 20. Group Sequential Tests for Treatment Effect with Covariates Adjustment through Simple Cross-Effect Models 311 Isaac Wu HONG-DAR 20.1. Introduction 311 20.2. Notations and models 313 20.3. Group sequential test 316 20.4. Discussion 318 20.5. Acknowledgment 318 20.6. Bibliography 318 PART 3 RELIABILITY AND MAINTENANCE 321 Chapter 21. Optimal Maintenance in Degradation Processes 323 Waltraud KAHLE 21.1. Introduction 323 21.2. The degradation model 324 21.3. Optimal replacement after an inspection 326 21.4. The simulation of degradation processes 327 21.5. Shape of cost functions and optimal δ and a 329 21.6. Incomplete preventive maintenance 330 21.7. Bibliography 333 Chapter 22. Planning Accelerated Destructive Degradation Tests with Competing Risks 335 Ying SHI and William Q. MEEKER 22.1. Introduction 336 22.2. Degradation models with competing risks 338 22.3. Failure-time distribution with competing risks 341 22.4. Test planning with competing risks 342 22.5. ADDT plans with competing risks 344 22.6. Monte Carlo simulation to evaluate test plans 352 22.7. Conclusions and extensions 353 22.8. Appendix: technical details 354 22.9. Bibliography 355 Chapter 23. A New Goodness-of-Fit Test for Shape-Scale Families 357 Vilijandas BAGDONAVIC¡IUS 23.1. Introduction 357 23.2. The test statistic 358 23.3. The asymptotic distribution of the test statistic 359 23.4. The test 364 23.5. Weibull distribution 364 23.6. Loglogistic distribution 365 23.7. Lognormal distribution 366 23.8. Bibliography 367 Chapter 24. Time-to-Failure of Markov-Modulated Gamma Process with Application to Replacement Policies 369 Christian PAROISSIN and Landy RABEHASAINA 24.1. Introduction 369 24.2. Degradation model 370 24.3. Time-to-failure distribution 371 24.4. Replacement policies 376 24.5. Conclusion 381 24.6. Acknowledgment 381 24.7. Bibliography 382 Chapter 25. Calculation of the Redundant Structure Reliability for Agingtype Elements 383 Alexandr ANTONOV, Alexandr PLYASKIN and Khizri TATAEV 25.1. Introduction 383 25.2. The operation process of the renewal and repaired products 384 25.3. The model of the geometric process 386 25.4. Task solution 387 25.5. Conclusion 389 25.6. Bibliography 390 Chapter 26. On Engineering Risks of Complex Hierarchical Systems Analysis 391 Vladimir RYKOV 26.1. Introduction 391 26.2. Risk definition and measurement 392 26.3. Engineering risk 393 26.4. Risk characteristics for general model calculation 395 26.5. Risk analysis for short-time risk models 400 26.6. Conclusion 402 26.7. Bibliography 402 List of Authors 405 Index 409

About the Author :
Vincent Couallier is Associate Professor at Bordeaux Segalen University in France Léo Gerville-Réache is Associate Professor at Bordeaux 2 University in France. Catherine Huber-Carol is Professor Emeritus at Paris René Descartes University in France. Nikolaos Limnios is Professor at Compiègne University of Technology in France. Mounir Mesbah is Professor at University Pierre and Marie Curie in Paris, France.