The optimal scheme in type II progressive censoring with random removals for the Rayleigh distribution based on two-sample Bayesian prediction and cost function

A type II progressive censoring scheme is one of the censoring methods that is important in life-testing studies. This method of censoring allows the experimenter to withdraw some of the tested units at different stages of testing. One question that arises when designing a type II progressive censoring is how we can decide to remove several units from the test at each step? Different answers can be made to answer this question by considering different criteria. In this paper, assuming the censoring scheme is a random variable from Binomial distribution, we intend to obtain the optimal parameter for the distribution of censoring scheme when the distribution is the Rayleigh distribution by considering two criteria, the cost of testing and the Mean squared prediction error in the two-sample prediction problem. To illustrate the effectiveness of the results, a simulation study and a real data example are presented with the help of MATLAB software.