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Journal Article

Statistical Inference for Pr(Y < X): The Normal Case

Benjamin Reiser and Irwin Guttman
Technometrics
Vol. 28, No. 3 (Aug., 1986), pp. 253-257
DOI: 10.2307/1269081
Stable URL: http://www.jstor.org/stable/1269081
Page Count: 5
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Statistical Inference for Pr(Y < X): The Normal Case
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Abstract

This article examines statistical inference for Pr(Y < X), where X and Y are independent normal variates with unknown means and variances. The case of unequal variances is stressed. X can be interpreted as the strength of a component subjected to a stress Y, and Pr(Y < X) is the component's reliability. Two approximate methods for obtaining confidence intervals and an approximate Bayesian probability interval are obtained. The actual coverage probabilities of these intervals are examined by simulation.

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