Statistical inference of Type-I progressively censored step-stress accelerated life test with dependent competing risks

Abstract

This paper considers a step-stress accelerated dependent competing risks model under progressively Type-I censoring schemes. The dependence structure between competing risks is modeled by a general bivariate function, the cumulative exposure model is assumed and the accelerated model is described by the power rule model. The point and interval estimation of the model parameters and the reliability under normal usage level at mission time are obtained by using the maximum likelihood method and the asymptotic normal theory. We also consider the Bayesian estimators and the highest posterior density credible intervals based on conjugate priors, E-Bayesian, hierarchical Bayesian and empirical Bayesian methods. To illustrate the proposed methodology, the Marshall-Olkin bivariate exponential distribution is used to model the dependence structure between competing risks. A Monte Carlo simulation study and a real data analysis are presented to study the performance of different estimation methods.

Keywords:

• Step-stress accelerated life test
• dependent competing risks
• power rule model
• cumulative exposure model
• Bayesian estimation
• Gibbs sampling algorithm

Aknowledgement

The authors would like to thank the Editor and two anonymous reviewers for their valuable comments and suggestions on an earlier version of this manuscript which led to a considerable improvement in the presentation of the manuscript.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Nos. 71571144, 11701406, 11901134), the China Scholarship Council (No. 201806290048), the Humanities and Social Science Fund in Ministry of Education in China (18YJC910009).