Objective Bayesian analysis for the accelerated degradation model using Wiener process with measurement errors

Abstract

The Wiener process as a degradation model plays an important role in the degradation analysis. In this paper, we propose an objective Bayesian analysis for an acceleration degradation Wiener model which is subjected to measurement errors. The Jeffreys prior and reference priors under different group orderings are first derived, the propriety of the posteriors is then validated. It is shown that two of the reference priors can yield proper posteriors while the others cannot. A simulation study is carried out to investigate the frequentist performance of the approach compared to the maximum likelihood method. Finally, the approach is applied to analyse a real data.

Keywords

• accelerated degradation model
• objective bayesian analysis
• wiener process
• measurement errors
• jeffreys prior
• reference prior