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.