We construct bootstrap confidence intervals for reliability, R= P{X>Y}, where X and Y are independent normal random variables. One way ANOVA random effect models are assumed for the populations of X and Y, where standard deviations and are unequal. We investigate the accuracy of the proposed bootstrap confidence intervals and classical confidence intervals work better than classical confidence interval for small sample and/or large value of R.
In this paper, we obtain some a, pp.oximate confidence intervals for the reliability of the stress-strength model when the stress and strength each depend on some explanatory variables, respectively. Also we compare the confidence intervals via Monte Carlo simulation.
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