Uma abordagem bayesiana para modelos de degradação: a obtenção da distribuição preditiva a posteriori dos tempos de falha de unidades amostrais futuras e sob teste: a obtenção da distribuição preditiva a posteriori dos tempos de falha de unidades amostrais futuras e sob teste

Abstract

Reliability is a branch of Statistical inference which seeks to describe the route failure time distribution of objects of interest. The conventional techniques are geared towards the occurrence of failures over time. However, for certain situations in which the occurrence of failures is small or almost zero, the estimation of quantities that describe the failure time is compromised. Thus, degradation models were developed, which the experiemtal data are not failures, but some measurable characteristic linked to them, which when monitored make possible significant improvements in estimates of quantities of interest. The degradation models have been widely applied and studied from the perspective of classical statistics, however, computational difficulties and misspecifications of the assumptions of the models, have turned interesting the approach by a focus on bayesian statistics. This is due to the fact that the computational methods implemented in the bayesian approach already allowed accommodate a larger number of probability distributions, thus become less susceptible to problems of misspecification. This text shows that even under misspecification the Bayesian approach can produce good results. The proposal in this paper is to point out some methodological errors that have been committed in the use of bayesian inference and present a proposal for anallyzing degradation paths, comparing it to the approaches for bayesian inference in the literature on degradation models. A database of laser emitters and another of train wheels illustrate the application of the methodology proposed in this text. The results allow to raise the reliability of the studied objects and future objects outside the scope of the sample.