Objective Bayesian analysis accelerated degradation test based on Wiener process models

Abstract

Constant-stress accelerated degradation test (CSADT) as an effective model is widely used in assessing product reliability when measurements of degradation leading to failure can be observed. We model the degradation process as a Wiener process. In this paper, we make inferences about the parameters of the CSADT using an objective Bayesian method. The noninformative priors (Jefferys prior and two reference priors) are derived, and we show that their posterior distributions are proper. Since the posterior distributions are very complicated, Gibbs sampling algorithms for the Bayesian inference based on the Jefferys prior and two reference priors are proposed. Some simulation studies are conducted to show the effectiveness of the objective Bayesian analysis. Finally, we apply the objective Bayesian method to a real data set and estimate the mean-time-to-failure (MTTF) under use condition.