| The Kaplan-Meier estimator is a well-known estimator for the empiric reliability when data are censored. In Part 1, we find exact expressions for the expectation and mean-square error of both the Kaplan-Meier estimator and the Nelson-Aalen estimator of the hazard function, assuming that censoring is random. We derive improved and easily computed upper bounds for the bias and the mean-square error. In Section 1.5 we demonstrate the properties of some of these bounds by computing results for selected instances.; In Part 2, a procedure to find the exact system reliability is given. Barlow and Proschan exhibit a formula using the inclusion-exclusion method to compute the reliability of a coherent system with independent components. The difficulty in applying that formula is finding probabilities of intersections of k dependent events. Here we propose a simple technique to handle such dependence, which extends the use of the formula. |
