Reliability Analysis for Competing Failure Models with Weibull Units

A competing risks model based on the Weibull distribution is considered under progressively Type-II censoring with binomial removals. Since the best approximation algorithms do not perform well for small-size samples, Bayes analysis based on the Gamma prior distribution is derived by the Gibbs sampling method. Using the parametric bootstrap method as well as the Bayesian posterior distribution, we discuss the construction of confidence intervals for the parameters. Finally, some numerical results are discussed to compare the performance of different estimations. Our experimental results show that the Bayes method performs better than MLEs in the small sample case.