Optimal Number of Failures in Type II Censoring for Rayleigh Distribution

Abstract

Recently, Rayleigh distribution has received considerable attention in the statistical literature. This paper describes the Bayesian prediction of the ‎one parameter Rayleigh ‎‎distribution when the data are Type II censored data. Suppose we are planning to collect a Type II censored sample from the ‎one parameter Rayleigh distribution in order to find a point predictor for a future order statistic with smallest mean squared prediction error (MSPE) among other point predictors. Although, considering large values for failure numbers yields a point predictor with smaller MSPE, the average cost may increase considerably. One question arises here that “How many failure is enough?". The aim of this paper is finding the optimal value for number of failures in Type II censoring by considering two criteria, total cost of experiment and mean squared prediction error. Towards this end, we find the Bayesian point predictor for the parameter of distribution. Then, the optimal value for number of failures is obtained when the mean squared prediction error and the total cost of experiment are bounded. To show the usefulness of the obtained results, a simulation study is presented.