Análise hierárquica de múltiplos sistemas reparáveis

Abstract

The thesis has as objective to study certain aspects of the hierarchical modeling of data from several repairable systems. More specifically, the hierarchical power law process model is approached. The work developed in this thesis is presented in the form of two papers, as follows. Paper 1: Hierarchical modelling of power law processes for the analysis of repairable systems with different truncation times: An empirical Bayes approach In the data analysis from multiple repairable systems it is usual to observe both different truncation times and heterogeneity among the systems. Among other reasons, the latter is caused by different manufacturing lines and maintenance teams of the systems. In this paper, a hierarchical model is proposed for the statistical analysis of multiple repairable systems under different truncation times. A reparameterization of the power law process is proposed in order to obtain a quasi-conjugate bayesian analysis. An empirical Bayes approach is used to estimate model hyperparameters. The uncertainty in the estimate of these quantities are corrected by using a parametric bootstrap approach. The results are illustrated in a real data set of failure times of power transformers from an electric company in Brazil.Paper 2: Empirical Bayes and Jeffreys prior for the hierarchical power law process In this paper we discuss alternative methods to model the third stage of a hierarchical power law process for modelling of several repairable systems. We argue that the Jeffreys prior has some advantages with respect to an empirical Bayes alternative or a noninformative prior proposed in the literature. More specifically, our simulations showed that the coverages of the intervals produced by the Jeffreys method are better than the interval coverages produced by empirical Bayes and noninformative methods. We also illustrate our methods with a real data set analysis.