Advances in Stochastic Models for Reliablity, Quality and Safety

I: Lifetime Analysis.- 1. The Generalized Linnik Distributions.- 1.1 Introductory Example and Preliminaries.- 1.2 Assembling Discrete Linnik and Discrete Stable Distributions.- 1.3 Calculation of Probabilities.- 1.4 Characterization via Survival Distributions.- 1.5 Asymptotic Behaviour.- References.- 2. Acceptance Regions and Their Application in Lifetime Estimation.- 2.1 Confidence Bounds Based on Acceptance Regions.- 2.1.1 Basic notations.- 2.1.2 Confidence bound and system of acceptance regions.- 2.1.3 The algorithm "System of lower ?-acceptance regions".- 2.1.4 Quality of lower confidence bounds.- 2.1.5 Optimality of the algorithm.- 2.1.6 Quick determination vs. good quality.- 2.2 Confidence Bound for the Expectation of a Weibull Distribution.- 2.2.1 The model.- 2.2.2 Applying the algorithm "System of lower ?-acceptance regions".- 2.2.3 Quality of lower confidence bounds for the expectation.- References.- 3. On Statistics in Failure-Repair Models Under Censoring.- 3.1 Introduction.- 3.2 Survival Data Analysis Under Censoring.- 3.3 Nonparametric Estimators for RT(t).- 3.4 The Failure-Repair Model Under Censoring.- 3.4.1 The general model.- 3.4.2 Model under Koziol-Green assumption.- References.- 4. Parameter Estimation in Renewal Processes with Imperfect Repair.- 4.1 Introduction.- 4.2 A General Model.- 4.3 Specifications.- 4.4 Parameter Estimation in the General Model.- 4.4.1 Estimation of the parameters of failure intensity.- 4.4.2 A simple model for estimating the degree of repair.- References.- 5. Investigation of Convergence Rates in Risk Theory in the Presence of Heavy Tails.- 5.1 A Model in Risk Theory.- 5.2 Limit Theorem.- 5.3 Rates of Convergence.- References.- 6. Least Squares and Minimum Distance Estimation in the Three-Parameter Weibull and Fréchet Models with Applications to River Drain Data.- 6.1 Introduction.- 6.2 Least Squares and Minimum Distance Methods.- 6.2.1 General.- 6.2.2 Least squares and minimum distance estimators for the three-parameter Weibull model.- 6.3 Modelling of River Drain Data.- 6.3.1 The data.- 6.3.2 General.- 6.3.3 Analysis of river Danube data.- 6.3.4 Analysis of river Main data.- References.- II: Reliability Analysis.- 7. Maximum Likelihood Estimation With Different Sequential k-out-of-n Systems.- 7.1 Introduction.- 7.2 Sequential k-out-of-n Systems With Unknown Model Parameters.- 7.3 Estimation in Specific Distributions.- 7.4 Sequential k-out-of-n Systems With Known Model Parameters and Underlying One-Parameter Exponential Family.- 7.5 Example: Sequential 2-out-of-4 System.- References.- 8. Stochastic Models for the Return of Used Devices.- 8.1 Introduction.- 8.2 Additive Models for Returns.- 8.3 Model Fit.- References.- 9. Some Remarks on Dependent Censoring in Complex Systems.- 9.1 Introduction and Summary.- 9.2 Dependence of the Components Within a Parallel System.- 9.2.1 Estimation of F by means of Fjk.- 9.2.2 Estimation of F by means of the Kaplan-Meier estimators of Fj.- 9.2.3 Estimation of F by means of multivariate Kaplan-Keier estimators.- 9.3 Dependence of the Lifelengths and their Censoring Variables.- References.- 10. Parameter Estimation in Damage Processes: Dependent Observations of Damage Increments and First Passage Time.- 10.1 Introduction.- 10.2 The Likelihood Function if Both Damage Increments and Failure Time are Observed.- 10.3 An Example.- 10.4 Appendix: Proof of Lemma 10.2.1.- References.- 11. Boundary Crossing Probabilities of Poisson Counting Processes with General Boundaries.- 11.1 Introduction.- 11.2 The Homogeneous Poisson Process.- 11.2.1 Upper boundary case.- 11.2.2 Lower boundary case.- 11.2.3 Two boundary case.- 11.3 The Nonhomogeneous Poisson Process.- 11.4 A Special Mixed Poisson Process.- References.- 12. Optimal Sequential Estimation for Markov-Additive Processes.- 12.1 Introduction.- 12.2 The Model and Sampling Times.- 12.3 Efficient Sequential Procedures.- 12.4 Minimax Sequential Procedures.- References.- 13. Some Models Describing Damage Proces