The purpose of this paper is to present a new procedure for selecting a population with the largest location parameter out of the
k given populations when the largest location parameter exceeds the second largest by a given length. The criterion for the optimality of the procedure is that the probability of the correct selection (PCS) is not less than a certain preassigned value. The procedure we consider in this paper is based on a rank sum statistics and PCS function is obtained at first for general
k populations. Then the problem is investigated more deeply on the case
k=2 and the table of PCS for our procedure, asymptotic property, and numerical comparisons of our procedure to asymptotic case and mean procedure are given.
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