A statistical inference for generalized Rayleigh model under Type-II progressive censoring with binomial removals

This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-II censoring with random removals, that is, the number of units removed at each failure time follows the binomial distribution. The maximum likelihood estimation and the Bayesian estimation are derived. In the meanwhile, through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure. A real industrial case is presented to justify and illustrate the proposed methods. We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.