A Two-Stage Minimax Decision Procedure for Selecting the Best of k Binomial Processes or Populations

Abstract Industrial development planners and decision makers quite often encounter the problem which one of several alternatives (processes, plans, brands, machines, varieties, etc.) is the best. This paper presents a statistical two-stage decision procedure for selecting the best of k (≥2) binomial processes or populations with the highest probability of obtaining a “success” on a single trial. In a first stage, preassigned number of n 1 observations are taken from each of k populations and a subset-selection is made for screening the populations. In the second stage, more n 2 observations are taken from each of the subset selected in the first stage and a final selection is made on the basis of observations obtained in the first and the second stages. The problem is how to determine the subset-selection rule at the first stage and the number of observations n 1 and n 2 required for selecting the best one with a specified probability P*. This problem is formulated from the indifference zone point of view...