A curtailed selection procedure for comparing Bernoulli outcomes with a control

A sequential selection procedure is proposed for comparing $k(>1)$ 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 $k+1$ 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.