Estimation of the reliability function of a series system: Some decision theoretic results

Consider a series system consisting of k-independent components. Assuming t hat the life time of the ith component follows an exponential distribution with failure rate Xi, i = 1, 2,..., k, we address the problem of point esti mation of the reliability of the system at a certain time point t > 0. Moti vated by a numerical study, we investigate the second order risk of the max imum likelihood estimator of the system reliability and establish its secon d order admissibility. We have also studied the unique minimum variance unb iased estimator and two popular generalized Bayes' estimators which turn ou t to be inferior to the MLE in terms of the first order mean squared error.