An infinite class of decision rules having several desirable properties is suggested for choosing a group of populations from a given set of normal populations which should contain the population with the largest mean. The problem of selecting one member from this infinite class of rules has also been studied.
K. C. Seal. "On a Class of Decision Procedures for Ranking Means of Normal Populations." Ann. Math. Statist. 26 (3) 387 - 398, September, 1955. https://doi.org/10.1214/aoms/1177728486