Empirical estimators for multi-component conditional stress-strength parameter

In many of reliability models, there exist certain information about the strength and stresses that experienced by the system. We are interested in how the model functions via these extra information or whether employing them does improve the performance of the system. In the present study the conditional stress-strength parameter have been investigated for s of k systems and the multi-component conditional stress-strength parameter (MCCSSP) has been estimated by using the Bayesian and non-parametric methods. In the case of having extra information about the parameters of the system, a closed form has been derived for the Bayes estimator of MCCSSP and has been calculated by using an algorithm together with Monte Carlo method. For simplicity, it has been done under the assumption of exponential distributions for the strength and stress random variables and gamma conjugates. For the case of non-exponential or general stress or strengths, the nonparametric estimator of the considered parameter has been derived. Finally to verify the analytic results, some simulation study for the Bayes estimator as well as nonparametric estimation of a real data set and some comparisons have been done.