Robustness of the probability of correct selection against deviations from the assumption of a common knwon variance

In this paper we investigate the robustness of the probability of correct selection against departures from the assumption of a common known variance for the Indifference Zone approach (cf. BECHHOFER (1954)), as well as for the Subset Selection approach (cf. GUPTA (1956, 1965)) in the case of Normal populations. It appears that there is a serious lack of robustness in the sense that the actual lower bound of the probability of correct selection can be considerably smaller than the pretended lower bound P* of the probability of correct selection based on the assumption of a common known variance, if P* is taken 0.75, 0.90, 0.95 and 0.99, respectively.