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

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.