Many authors have formulated the Bayes estimation under type I progressive censored for the mixed model without the conditions set by Mendenhall and Hader [16]. In this article, we will modify the Bayes estimation in order to be consistent with the conditions for mixture model. Estimators will be compared in the case of neglecting or taken into consideration the conditions of mixed distributions. The parameters of the Rayleigh mixture are estimated and compared using the Bayes estimates under the square error loss function and LINEX loss functions to illustrate the difference between the estimators and their explanations. Comparisons are made between two models via a Monte Carlo simulations study.

finite mixture, type I progressive censored, Rayleigh distribution, likelihood function, Bayes estimates, square error loss function, LINEX loss functions, Monte Carlo simulations.