‎Nowadays inference based on censored samples has been studied by many researchers‎. ‎One of the most common censoring methods is progressively type II censoring‎. ‎In this model‎, ‎n items are put on the test‎. ‎At each failure times some of the remaining items randomly withdrawn from the test‎. ‎This process continues until for a pre-fixed value as m, ‎failure times of m items are observed‎. ‎For determining the best number for the items on the test different criteria can be considered‎. ‎One of the most important factors that can be considered is the cost criterion‎. ‎In this paper‎, ‎by considering cost function and Weibull distribution for the lifetime of items‎, ‎we find the optimal value for the sample size‎, ‎i.e‎. n‎. ‎In order to evaluate‎, ‎the obtained results one example based on real data is given‎. 

The empirical Bayes estimation of the exponential distribution parameter under squared error and LINEX loss functions is investigated when the record collects the data ranked set sampling scheme method. Then, point and interval predictions for future record values are studied. The results of this sampling scheme are compared with the products of the inverse sampling scheme. To compare the accuracy of estimators, Bayes risk and posterior risk criteria are used. These point predictors are compared in the sense of their mean squared prediction errors. To evaluate the prediction intervals for both the sampling schemes, the average interval length and coverage probability are computed and compared. In the present study, the hyperparameters are estimated in two methods. By studying the simulation and presenting real data, the estimation methods are compared, and the performance of the introduced schemes is evaluated.