Bayes analysis of one-shot device testing data with correlated failure modes using copula models

Abstract

Copula models are capable of modeling the dependence structure among the random variables, a phenomenon that is often required in the statistical analysis. Such models are the flexible substitutes of multivariate distributions because they model both the marginal distributions and the joint dependence structure distinctly. Because of such important features, the models are recognized as popular tools in a variety of situations including reliability engineering and survival analysis. The present paper studies a Bayesian approach using three Archimedean copulas, namely, the Gumbel Hougaard copula, the Frank copula and the Joe copula for analyzing one-shot device testing data with two correlated failure modes collected from a constant stress accelerated life test. One-shot devices are units that can be used only once and destroyed immediately after the use. Obviously, one obtains either left or right censored data on the failure times instead of actual failure times of the devices. Finally, all the considered copula models are compared using the Bayesian model selection tools. A real dataset is analyzed as an illustration of the proposed Bayesian methodology.

Keywords:

• Accelerated life test
• Bayesian inference
• Bayes information criterion
• Deviance information criterion
• Frank copula
• Gumbel Hougaard copula
• Joe copula
• One-shot devices

Acknowledgments

The authors express their thankfulness to the editor and the referees for their valuable comments and suggestions that improved the earlier version of the manuscript. The research work of Dr. Reema Sharma is partially supported by the seed grant sanctioned under the IoE scheme of Banaras Hindu University.

Disclosure statement

No potential conflict of interest was reported by the author(s).