Inference for a simple step-stress model with progressively censored competing risks data from Weibull distribution

ABSTRACT

In reliability analysis, it is common to consider several causes, either mechanical or electrical, those are competing to fail a unit. These causes are called “competing risks.” In this paper, we consider the simple step-stress model with competing risks for failure from Weibull distribution under progressive Type-II censoring. Based on the proportional hazard model, we obtain the maximum likelihood estimates (MLEs) of the unknown parameters. The confidence intervals are derived by using the asymptotic distributions of the MLEs and bootstrap method. For comparison, we obtain the Bayesian estimates and the highest posterior density (HPD) credible intervals based on different prior distributions. Finally, their performance is discussed through simulations.

KEYWORDS:

• Competing risks
• confidence/credible interval
• MLEs and Bayesian estimates
• proportional hazard model
• progressive censoring
• simple step-stress model.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N01
• 62N02

Acknowledgments

The authors are grateful to the referees and editors for their helpful comments, which had improved significantly the manuscript.

Funding

This research is supported by the National Natural Science Foundation of China (numbers 71171164, 71401134, 71571144) and the Natural Science Basic Research Program of Shaanxi Province (number 2015JM1003).