Uma abordagem dinâmica para o modelo linear de degradação sob a perspectiva bayesiana

Abstract

Much of the literature on Reliability deals with data where the observed measure is the failure time of the units under test. However, for situations with little or no failure, the inference in this approach can be compromised. In this context, an alternative is the use of degradation data, where measures of some inherent characteristic of the failure are collected in the units at pre-specied and distinct times and it is dened that the failure occurs when this mechanism exceeds a critical threshold of degradation stipulated. In the general degradation path models, considering that the functional form can be approximated by a linear relationship between degradation and time, the linear degradation model is obtained. Nevertheless, by assuming that the degradation rates of the units under test are constant over time, this model may be inadequate for data analysis in which the occurrence of some change in the structure of the process under investigation or the omission of certain variables may justify instability in degradation rates. Thus, the present text aims to extend the linear model of degradation with respect to its functional form by inserting a dynamic structure in the model from a bayesian perspective. That is, in the rst step of the approach, a linear dynamic model is tted in the units under test incorporating a system evolution component capable of better accommodating instabilities in the degradation rates that occur during the conduction of the tests. The proposed methodology is then compared with the linear model of degradation through simulation studies and the application to three real databases. The results pointed to the importance of taking into account the dynamics of the degradation proles in the analysis of the time distribution until the failure of the units.