A Distribution-Free Upper Confidence Bound for $\Pr \{Y < X\}$, Based on Independent Samples of $X$ and $Y$

A solution for the problem of obtaining a distribution-free one-sided confidence interval for $p = \Pr \{Y < X\}$ has been proposed in [1]. At present a numerical procedure is given for computing the sample sizes needed for such a confidence interval with given width and confidence level.