Estimation of Reliability of Stress-strength for a Kumaraswamy Distribution based on Progressively Censored Sample‎

‎The estimation of R=P(X<Y) in the case that X and Y are two independent Kumaraswamy distributed random variables with different parameters for progressively Type-II censored samples is studied‎. ‎First assuming the same second shape parameters of two distributions‎, ‎the maximum likelihood estimation and different confidence intervals are considered‎. ‎Moreover‎, ‎in case the second shape parameters of two distributions are known‎, ‎MLE‎, ‎UMVUE‎, ‎Bayes estimation of R and confidence intervals are derived‎. ‎Finally‎, ‎the Maximum Likelihood and Bayes estimations of R in general case are obtained‎. ‎Performance comparisons of different methods are carried out utilizing Monte Carlo simulations‎. ‎Besides‎, ‎the proposed approach is employed for reliability analysis on a real strength-stress dataset to demonstrate its application‎.