Inference on Weibull parameters under a balanced two-sample type II progressive censoring scheme

The progressive censoring scheme has received considerable amount of attention in the last fifteen years. During the last few years joint progressive censoring scheme has gained some popularity. Recently, the authors Mondal and Kundu ("A new two sample Type-II progressive censoring scheme", arXiv:1609.05805) introduced a balanced two sample Type-II progressive censoring scheme and provided the exact inference when the two populations are exponentially distributed. In this article we consider the case when the two populations follow Weibull distributions with the common shape parameter and different scale parameters. We obtain the maximum likelihood estimators of the unknown parameters. It is observed that the maximum likelihood estimators cannot be obtained in explicit forms, hence, we propose approximate maximum likelihood estimators, which can be obtained in explicit forms. We construct the asymptotic and bootstrap confidence intervals of the population parameters. Further we derive an exact joint confidence region of the unknown parameters. We propose an objective function based on the expected volume of this confidence set and using that we obtain the optimum progressive censoring scheme. Extensive simulations have been performed to see the performances of the proposed method, and one real data set has been analyzed for illustrative purposes.