• Journal of the Korean Statistical Society
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• v.27 no.4
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• pp.435-449
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• 1998

In this paper, we consider the problem of constructing the lower cofidence intervals for the reliability P(X < Y z,w), where the stress X and the strength Y are the random variables with explanatory variables z and w, respectively. As an estimator of the reliability, a Mann-Whitney type statistic is considered. It is shown that under regularity conditions, the proposed estimator is asymptotically normal. Based on the result, the distribution free lower confidence intervals are constructed.

• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.73-85
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• 1996

In this paper, we consider the distribution-free confidence intervals for the reliability of the stress-strength model when the stress X and strength Y depend linearly on some explanatory variables z and w, respectively. We apply these confidence intervals to the Rocket-Motor data and compare the results to those of Guttman et al. (1988). Some simulation results show that the distribution-free confidence intervals have better performance for nonnormal errors compared to those of Guttman et al. (1988), which are designed for normal random variables in respect that the former yield the coverage levels closer to the nominal coverage level than the latter.