Objective Bayesian Analysis for Linear Degradation Models

Abstract

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.

Keywords:

• Degradation data
• Objective Bayes
• Reference prior

Mathematics Subject Classification:

• Primary 62F15
• Secondary 62N05

Acknowledgment

This research is supported by the National Natural Science Foundation of China (11201345). The authors thank the two referees for their constructive suggestions that greatly improved the article.