A curtailed selection procedure for comparing Bernoulli outcomes with a control

A sequential selection procedure is proposed for comparing (Formula presented.) experimental Bernoulli populations with a controlled Bernoulli population. The comparison is made according to the success probability. Based on the numbers of successes of the (Formula presented.) populations, the indifference zone formulation and the subset selection formulation are integrated to select either the best population or a random-sized subset that contains the best population. Observations are taken one at a time and the populations that are no longer comparable are eliminated until either the best is identified or the total number of observations in at least one population reaches a specific upper bound. We show that the proposed sequential procedure satisfies the same probability requirements as does the corresponding fixed-sample-size procedure. Furthermore, the expected sample size from each population for the proposed procedure is significantly smaller than the sample size required by the fixed-sample-size procedure.