Estimation of multicomponent stress-strength reliability for exponentiated Gumbel distribution

In this paper, the stress-strength reliability R-s,R-k of a multicomponent s-out-of-k system for exponentiated Gumbel distribution is considered. An s-out-of-k system means a system with total k components and the system can survive only when atleast s of the total components function properly. The ability of the system to overcome the experiencing stress with its strength is termed as its stress-strengh reliability. The maximum likelihood estimator and Bayes estimator for R-s,R-k are obtained. The Bayes estimators are obtained using Markov chain Monte Carlo(MCMC) method under both symmetric and asymmetric loss functions. The loss functions we considered are squared error loss function, LINEX loss function and entropy loss function. The asymptotic, bootstrap and highest posterior density(HPD) confidence intervals for R-s,R-k are also obtained. A simulation study is conducted for evaluating the efficiency of the estimators derived in this paper. Real data sets are also considered for illustration.