An integrated formulation for selecting the t best of k normal populations

We refer to the two classical approaches to ranking and selection as the indifference zone approach and the subset-selection approach. This paper integrates those two approaches by separating the parameter space into two disjoint parts, the preference zone < PZ} and the indifference zone (IZ). In the PZ we insist on selecting the t best for a correct selection (CS) but in the IZ we define any se1ected subset to be correct (GS₀) if it contains the t best populations. We then use different methods to find two constants and a common sample size n that simultaneously give lower bounds P-, for (CSj|PZ) and Pn for P(CS₀|IZ). Here the values of, PQ and 6 (which defines the PZ) are all specified and can be arbitrarily close to 1, 1 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 configuration (EPC). It is shown that the former is least favorable in the PZ and, for t = 1, that the latter is the worst case in the IZ. An illustrative example is included, but extensive tables have not vet been developed.