Reliability estimation based on ranked set sampling

Emad El-Neweihi and Bikas K. Sinha

Communications in Statistics - Theory and Methods, 2000, vol. 29, issue 7, 1583-1595

Abstract: In this paper we consider the problem of estimating the reliability of an exponential component based on a Ranked Set Sample (RSS) of size n. Given the first r observations of that sample, 1≤r≤n, we construct an unbiased estimator for this reliability and we show that these n unbiased estimators are the only ones in a certain class of estimators. The variances of some of these estimators are compared. By viewing the observations of the RSS of size n as the lifetimes of n independent k-out-of-n systems, 1≤k≤n, we are able to utilize known properties of these systems in conjunction with the powerful tools of majorization and Schur functions to derive our results.

Date: 2000
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DOI: 10.1080/03610920008832566

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