Abstract
The stochastic process models are treated to estimate 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 with the Markov chain Monte Carlo method. In addition, the estimation methods based on the empirical Bayesian, the maximum likelihood, and the generalized moment are also appropriated to the models. The information criterion EIC is used to select a fitted model among the stochastic models with the estimation procedures. The marginal likelihood with the Laplace’s method plays important roles in the methodologies proposed in this paper. In this paper, the Bayesian method with prior distributions is emphasized to apply expert opinions based on engineers for the reliability analysis. It is proposed that an expert opinion adopted to the analyzed phenomenon is chosen by using the information criterion EIC.
