‎In this paper‎, ‎we study the ‎prediction problem in the two-sample case for predicting future progressively Type-II censored order statistics based on observed progressively Type-II censored order statistics with random removals from the Rayleigh distribution‎. ‎We consider two important distributions for random removals‎, binomial and discrete uniform distributions‎. ‎In both cases‎, ‎Bayesian point and interval predictors are obtained‎. ‎In the following‎, ‎through a simulation study‎, ‎the results are compared to each other‎. ‎Finally‎, ‎a real data set is given to textcolor{red}{illustrate} the output results‎.