Statistics and Its Interface

Volume 12 (2019)

Number 2

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

Pages: 295 – 307

DOI: https://dx.doi.org/10.4310/SII.2019.v12.n2.a10

Authors

Lei He (Department of Statistics, Anhui Normal University, Wuhu, China)

Dongchu Sun (Department of Statistics, University of Missouri, Columbia, Mo., U.S.A.; and Department of Statistics, East China Normal University, Shanghai, China)

Daojiang He (Department of Statistics, Anhui Normal University, Wuhu, China)

Abstract

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 constantstress 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.

Keywords

accelerated degradation test, inverse Gaussian process, mean-time-to-failure, objective Bayes

2010 Mathematics Subject Classification

Primary 62F15. Secondary 62N05.

Received 10 March 2018

Published 11 March 2019