Application of statistical inference for partially ordered hypotheses

In quality control and decision support systems, ranking and selection are very important, because we often encounter situations in which we need to rank several objects and to select some out of them. We investigate a problem of ranking k(⪰ 2) independent normal populations and selecting superior or inferior m(≤ k) out of them. The purpose of this paper is to formulate the problem as that of statistical hypothesis test, and to give critical values for practical use. We present computational methods for the level probabilities, which are needed for finding the critical values.