Inhaltsangabe
I: Statistical Methods.- 1 Statistical Modeling and Analysis of Repairable Systems.- 1.1 Introduction.- 1.2 "Major Events" in the History of Repairable Systems Reliability.- 1.3 Notation and Basic Definitions.- 1.4 Classification of Repair Actions.- 1.5 The Trend-Renewal Process.- 1.6 Statistical Inference in Trend-Renewal Processes.- 1.7 Trend Testing.- 1.8 Monte Carlo Trend Tests.- 1.9 Concluding Remarks and Topics for Further Study.- References.- 2 CPIT Goodness-of-Fit Tests for Reliability Growth Models.- 2.1 Introduction.- 2.2 The Conditional Probabilty Integral Transformation.- 2.3 CPIT GOF Tests for the Homogeneous Poisson Process.- 2.4 CPIT GOF Tests for the Jelinski-Moranda and Goel-Okumoto Models.- 2.5 CPIT GOF Tests for the Power-Law Process.- 2.6 Experimental Results.- 2.7 Conclusion.- References.- 3 On the Use of Minimally Informative Copulae in Competing Risk Problems.- 3.1 Competing Risk.- 3.2 Bounds Without Assumptions on a Dependence Structure.- 3.2.1 Peterson bounds.- 3.2.2 Crowder-Bedford-Meilijson bounds.- 3.3 Estimators Using Dependence Assumptions.- 3.3.1 The copula-graphic estimator.- 3.4 Minimallly Informative Copulae.- 3.5 Examples.- 3.5.1 Example 1.- 3.5.2 Example 2.- 3.6 Conclusions.- References.- 4 Model Building in Accelerated Experiments.- 4.1 Introduction.- 4.2 Additive Accumulation of Damages Model and Its Submodels.- 4.3 Generalized Multiplicative Models.- 4.4 Generalized Additive and Additive-Multiplicative Models.- 4.5 Models Describing the Influence of Stresses to the Shape and Scale of Distribution.- 4.6 The Model of Sedyakin and Its Generalizations.- 4.7 The Heredity Hypothesis.- References.- 5 On Semiparametric Estimation of Reliability From Accelerated Life Data.- 5.1 Introduction.- 5.2 Estimation in the AAD Model.- 5.3 Properties of Estimators.- 5.4 Estimation, When Stresses Change the Shape of Distribution.- 5.5 Estimation in AFT Model, When G is Completely Unknown and r is Parametrized.- References.- 6 Analysis of Reliability Characteristics Estimators in Accelerated Life Testing.- 6.1 Introduction.- 6.2 Parametric Estimation.- 6.3 Nonparametric Estimation.- 6.4 Conclusion.- References.- 7 Chi-Squared Goodness of Fit Test for Doubly Censored Data With Applications in Survival Analysis and Reliability.- 7.1 Introduction.- 7.2 Weak Convergence of the Process Un(t).- 7.3 The Weak Convergence of the Process Un*(t).- 7.4 The Test Statistics.- References.- 8 Estimation of Kernel, Availability and Reliability of Semi-Markov Systems.- 8.1 Introduction.- 8.2 Estimator of the Semi-Markov Kernel.- 8.3 Estimation of the Markov Renewal Matrix and Its Asymptotic Properties.- 8.4 Estimation of the Semi-Markov Transition Matrix and Its Properties.- 8.5 Reliability and Availability Estimation.- 8.5.1 Availability.- 8.5.2 Reliability.- 8.5.3 Asymptotic properties of the estimators.- 8.6 Application.- References.- II: Probabilistic Methods.- 9 Stochastical Models of Systems in Reliability Problems.- 9.1 Introduction.- 9.2 Reliability Problem for a Redundant System.- 9.2.1 Repairable duplicated system.- 9.2.2 Sojourn time in a subset of states.- 9.3 Problems of Singular Perturbation.- 9.4 Analysis of Stochastic Systems.- 9.4.1 Phase merging scheme.- 9.4.2 Heuristic principles of phase merging.- 9.5 Diffusion Approximation Scheme.- References.- 10 Markovian Repairman Problems. Classification and Approximation.- 10.1 Introduction.- 10.2 Classification of Repairman Models.- 10.3 Asymptotical Analysis of Queueing Process.- References.- 11 On Limit Reliability Functions of Large Systems. Part I.- 11.1 Introduction.- 11.2 Limit Reliability Functions of Homogeneous Systems.- 11.3 Limit Reliability Functions of Nonhomogeneous Systems.- 11.4 Remarks on Limit Reliability Functions of Multi-State Systems.- 11.5 Summary.- References.- 12 On Limit Reliability Functions of Large Systems. Part II.- 12.1 Domains of Attraction of Limit Reliability Functions.- 12.2 Asymptotic Reliability Functions of a Regular Homogeneous
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