Assessing System Reliability Using Censoring Methodology.
STANFORD UNIV CA DEPT OF STATISTICS
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This document describes a problem which is of practical and theoretical importance in reliability. Under study is a coherent structure consisting of n independent components. The structure is observed continuously until it fails. For components failing before or at system failure time, we observe complete lifelengths for components still functioning at system failure time we observe censored lifelengths. For the system we observe system lifelength. From a sample of m such structures we wish to estimate the system lifelength distribution. As far as we know, this problem has not been solved or even treated in the literature. In this paper we propose an estimator of the system lifelength distribution. as a by-product, we also obtain estimates of the mean and quantiles of the system lifelength and of all the corresponding quantities for component lifelengths. In Section 2 we give several asymptotic results concerning the estimators. In Section 3 we present and discuss two boot-strap schemes that are used in small samples to assess the variability of our estimates and to construct confidence intervals. Keywords Statistics Censored data.
- Statistics and Probability