An Integrated Formulation For Selecting The t Best Of k Normal Populations

Abstract

We refer to the two classical approaches to ranking and selection as the indifference zone approach and the subset selection approach. This paper integrates these two appraches by separating the parameter space into two distionit parts, the preference zone (PZ) and the indifference zone (IZ). In the PZ we insist on selecting the t best for a correct selection (CS1) but in the IZ we define any selected. We then use different methods to find two constants and a common sample size n that simultaneously give lower bounds P1 for (CS1PZ) and Po for P(CS2IZ). Here the values of P1. Po snf (which defines the PZ) are all specified and can be arbitraily close to 11 and 0, respectively. Explicit results are given for the P(CS), E(S), P(S=k) and P(S=t), especially for the slippage configuration (SPC) and the equal parameter configuratim (EPC). It is shown that the former is least favorable in the PZ and, for t = l, that the latter is the worst case in the IZ. An illustrative exmple is included, but extensive tables have not vet developed receiveddate="Dec1985" reviseddate="Jun1986"