Objective bayesian analysis for linear degradation models

We propose an objective Bayesian approach to analyze degradation models. For the linear degradation models, two reference priors are derived, and based on this we show the posterior distributions are proper. Since the lifetime of the product is of interest in practice, a transformation is introduced to obtain the reference priors of the medium lifetime. In the posterior analysis, we explore two sampling procedures: Monte Carlo (MC) procedure and Monte Carlo Markov Chain (MCMC) procedure. A real data from Takeda and Suzuki (1983) is analyzed, and we find the results obtained by both procedures are close to the given literature.