On the performance characteristics of a closed adaptive sequential procedure for selecting the best bernoulli population

Abstract
In a recent paper, Bechhofer and Kulkarni proposed closed adaptive sequential procedures for a general class of k—population Bernoulli selection goals. These sequential selection procedures achieve the same probability of a correct selection, uniformly in the unknown single—trail "success" probabilities , as do the corresponding single—stage selection procedures which take exactly n observations from each of the k populations. The sequential procedures always require less (often substantially less) than kn observations to terminate experimentation. This earlier paper described the procedures, discussed their performance in general terms, and cited several of their optimality properties. In the present paper we specialize these procedures, and focus on the particular goal of selecting the population associated with p[k] where are the ordered .Stronger optimality results than those given in our earlier paper are cited. We give exact numerical results for such performance characteristics of the sequential procedure (p*) as the distribution of the total number of observations N (i) taken from the population associated with and the total number of observations taken from all k populations, when the procedure terminates sampling. A simple upper bound for is given. These results along with other related ones will assist the potential user of the sequential procedure in assessing its merits relative to those of other competing procedures.