ABSTRACT

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.

摘要

提出了一种顺序选择程序来比较 $克(>1)$具有受控伯努利种群的实验伯努利种群。根据成功概率进行比较。根据成功的次数$克+1$人口，无差异区公式和子集选择公式被整合以选择最佳人口或包含最佳人口的随机大小的子集。一次进行一个观察，并消除不再具有可比性的群体，直到确定最佳群体或至少一个群体中的观察总数达到特定上限。我们表明，所提出的顺序程序满足与相应的固定样本大小程序相同的概率要求。此外，建议程序的每个总体的预期样本量明显小于固定样本量程序所需的样本量。