Análise de referência Bayesiana para o modelo Weibull na aplicação de riscos competitivos

Abstract

There are situations where various risk factors of failure are present, in the same time, in the life of system. For this reason we say that these factors are competing to cause the system failure. However, only one of these competitors is responsible for the system failure. The failure behavior of one system is, in most times, represented for its failure rate, which may be increasing, decreasing, remain constant or be combinations of these over time. Therefore it is desirable to use a probabilistic model that only with changes in the values of the parameters representing each of these situations. In this work we studied from the perspective of Bayesian reference analysis to the application of competitive risks under the Weibull model due to high flexibility of this model. The reference analysis is a method to produce Bayesian inferential statements which only depend on the assumed model and the available data (Bernardo, 1979). The goal is to find a specific joint reference prior function for all the unknown parameters of Weibull model in the application of competitive risks and a marginal reference posterior to the parameters of interest, which is always dominated by the observed data. The reference posterior distributions are obtained through the use of the Bayes theorem with the reference prior function that can be used to point estimates and tests of hypotheses, providing a unified set of Bayesian objective solutions for our problem.