A competing risks model based on Burr-XII distributions is considered under progressively first-failure censoring. Based on this type of censoring, we derive the Bayes estimators for the unknown parameters. When the common shape parameter is known, Bayes estimators with respect to the squared error loss (SEL) function can be obtained in the explicit closed form and the corresponding credible intervals also can be constructed explicitly. As expected, when the common shape parameter is unknown, the explicit expressions of the Bayes estimators cannot be obtained. Hence, we propose Markov chain Monte Carlo (MCMC) method to compute the Bayes estimates and construct the credible intervals of the unknown parameters. One set of real data has been analyzed for illustrative purposes. Finally, we provide a Monte Carlo simulation to compare and select optimal censoring schemes.

Burr-XII distribution, progressive first-failure censoring, competing risks, MCMC method, credible intervals.