Applying the copula approach on step stress accelerated life test under type II censoring

Abstract

The copula approach is a way to describe the dependence structure between variables. This could be done through splitting the analysis of the joint distribution of a multivariate random vector into two parts: the analysis of the marginals and the analysis of a copula which describes the dependence structure. An important field of reliability in which the copula approach could be applied, is the accelerated life testing (ALT). When a test unit fails under ALT, there are often more than one fatal cause for the failure. In this paper, we consider the simple step-stress ALT (SSALT) under type II censoring when the lifetime distribution of the different risks are dependent. The dependence structure between the competing risks is described using the copula approach. The point estimates of the unknown parameters are obtained using the maximum likelihood method. Also, the interval estimates for the unknown parameters are constructed using the asymptotic distributions and the parametric bootstrap method. Numerical analysis including simulated data and a real life data set is conducted to study the performance of the estimates.

Keywords:

• Competing risks
• Copula
• Maximum likelihood
• Step-stress accelerated life test
• Type II censoring

Acknowledgements

The authors thank the editor and anonymous reviewer for their comments and suggestions which led to an improved presentation of the paper.