System reliability estimation in multicomponent exponential stress-strength models

A stress-strength model is formulated for a multi-component system consisting of k identical components. The k components of the system with random strengths ($X_1$, $X_2$, ${\ldots}$, $X_k$) are subjected to one of the r random stresses ($X_{k+1}$, $X_{k+2}$, ${\ldots}$, $X_{k+r}$). The estimation of system reliability based on maximum likelihood estimates (MLEs) and Bayes estimators in k component system are obtained when the system is either parallel or series with the assumption that strengths and stresses follow exponential distribution. A simulation study is conducted to compare MLE and Bayes estimator through the mean squared errors of the estimators.