Estimation of multicomponent stress-strength reliability for exponentiated Gumbel distribution using ranked set sample

This paper investigates stress-strength reliability, denoted as Rs, k, of a multicomponent s-out-of-k system for an exponentiated Gumbel distribution using ranked set sampling method. The study discusses maximum likelihood and Bayesian estimation techniques for Rs, k. Bayes estimators are obtained under symmetric and asymmetric loss functions using Markov chain Monte Carlo method. Confidence intervals, including asymptotic, percentile bootstrap, and highest posterior density, for Rs, k are derived. A simulation study is performed to assess the efficiency of the proposed estimators, supplemented by the analysis of real data for illustration purposes.