In this paper a decision procedure based on the Tukey Studentized range (, , ) has been shown to be an optimum procedure for a particular type of slippage of means of univariate normal populations based on a common but unknown variance. The method given here is similar to that used by Paulson  and Truax .
"On a Decision Procedure Based on the Tukey Statistic." Ann. Math. Statist. 28 (3) 802 - 806, September, 1957. https://doi.org/10.1214/aoms/1177706897