Abstract
Consider a series system consisting of k-independent components. Assuming that the life time of the ith component follows an exponential distribution with failure rate λi, i = 1, 2, … , k, we address the problem of point estimation of the reliability of the system at a certain time point t > 0. Motivated by a numerical study, we investigate the second order risk of the maximum likelihood estimator of the system reliability and establish its second order admissibility. We have also studied the unique minimum variance unbiased estimator and two popular generalized Bayes' estimators which turn out to be inferior to the MLE in terms of the first order mean squared error.
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