Reliability Analysis for Degradation Data Based on Stochastic Process Models and Bayesian Estimations

Abstract

The Lévy process is considered to predict reliability assessments for degradation phenomena. In particular, the geometric Brownian motion and the gamma process models are handled, and the Bayesian procedures are applied to the models. The Markov chain Monte Carlo method and the empirical Bayesian method based on hierarchical Bayesian modeling are used to estimate the parameters. In addition, the maximum likelihood method and the generalized moment method are also appropriated to the models. The information criterion EIC is used to select a fitted model among the stochastic models and the estimation methods. The marginal likelihood with the Laplace's method plays important roles in the methodologies proposed in this paper.