In this paper, we propose a computer-oriented method of construction of optimal group sequential hypothesis tests with variable group sizes. In particular, for independent and identically distributed observations we obtain the form of optimal group sequential tests which turn to be a particular case of sequentially planned probability ratio tests (SPPRTs, Schmitz, 1993) . Formulas are given for computing the numerical characteristics of general SPPRTs, like error probabilities, average sampling cost, etc. A numerical method of designing the optimal tests and evaluation of the performance characteristics is proposed, and computer algorithms of its implementation are developed. For a particular case of sampling from a Bernoulli population, the proposed method is implemented in R programming language, the code is available in a public GitHub repository. The proposed method is compared numerically with other known sampling plans.

翻译：本文提出了一种计算机辅助的变分组规模最优组序贯假设检验构建方法。具体而言，针对独立同分布观测数据，我们推导出最优组序贯检验的形式，该形式可归为序贯计划概率比检验（SPPRTs, Schmitz, 1993）的特例。文中给出了计算一般SPPRT数值特征（如错误概率、平均抽样成本等）的公式，提出了最优检验设计及性能特征评估的数值方法，并开发了相应的计算机算法实现。以伯努利总体抽样为例，该方法通过R编程语言实现，相关代码已公开于GitHub仓库。最后，将所提方法与其他已知抽样方案进行了数值比较。