Bayesian Estimation Based on Rayleigh Progressive Type II Censored Data with Binomial Removals

This study considers the estimation problem for the parameter and reliability function of Rayleigh distribution under progressive type II censoring with random removals, where the number of units removed at each failure time has a binomial distribution. We use the maximum likelihood and Bayesian procedures to obtain the estimators of parameter and reliability function of Rayleigh distribution. We also construct the confidence intervals for the parameter of Rayleigh distribution. Monte Carlo simulation method is used to generate a progressive type II censored data with binomial removals from Rayleigh distribution, and then these data are used to compute the point and interval estimations of the parameter and compare both the methods used with different random schemes. 1. Introduction The Rayleigh distribution provides a population model which is useful in several areas of statistics. In the literature, many researcher studied properties of the Rayleigh distribution, particularly in life testing and reliability. Life testing experiments often deal with censored sample in order to estimate the parameters involved in the life distribution. The cumulative distribution function (CDF), probability density function (PDF), and the reliability function of the Rayleigh distribution with parameter are respectively. Inferences for in the Rayleigh distribution have been discussed by several authors. Harter and Moore [1] derived an explicit form for the maximum likelihood estimator (MLE) of based on type II censored data. Moreover, Bayesian estimation and prediction problems for the based on doubly censored sample have been considered by Fernández [2] and Raqab and Madi [3]. Wu et al. [4] have derived the Bayesian estimator and prediction intervals based on progressively type II censored samples. A recent account on progressive censoring schemes can be obtained in the monograph by Balakrishnan and Aggarwala [5] or in the excellent review article by Balakrishnan [6]. Suppose that units are placed on a life test and the experimenter decides beforehand quantity , the number of units, to be failed. Now at the time of the first failure, of the remaining surviving units are randomly removed from the experiment. Continuing, at the time of the second failure, of the remaining units are randomly drawn from the experiment. Finally, at the time of the th failure, all the remaining surviving units are removed from the experiment. Note that, in this scheme, are all prefixed. However, in some practical situations, these numbers may occur at random. For example, in some reliability