On a Conjecture of Bechhofer, Kiefer, and Sobel for the Levin–Robbins–Leu Binomial Subset Selection Procedures

Abstract We state a general formula that provides a lower bound for the probability of various types of acceptable subset selection with the Levin–Robbins–Leu binomial subset selection procedure without elimination or recruitment. We prove the truth of a conjecture of Bechhofer, Kiefer, and Sobel for this procedure by applying the general lower bound. We also introduce a simple modification that allows sequential elimination of inferior populations and recruitment of superior populations. Numerical evidence indicates that the new procedure also obeys the general lower bound while reducing the expected number of observations and failures compared with nonadaptive methods.