Objective Bayesian analysis for accelerated degradation data using inverse Gaussian process models

The inverse Gaussian (IG) process has become an important family in degradation analysis. In this paper, we propose an objective Bayesian method to analyze the constant-stress accelerated degradation test (CSADT) based on IG process model. Several commonly used noninformative priors, including the Jeffreys prior, the reference prior and the probability matching prior, are derived after reparameterization. The propriety of the posteriors under those priors is validated, among which two types of reference priors are shown to yield improper posteriors while the others can lead to proper posteriors. A simulation study is carried out to compare the proposed Bayesian method with the maximum likelihood one in terms of the mean squared errors and the frequentist coverage probability. Finally, the approach is applied to a real data example and the mean-time-to-failure of the product under the usage stress is estimated.