Abstract Regular fractional factorial designs with 2-level factors are among the most frequently used experimental plans. In many cases, designs should be blocked for dealing with inhomogeneity of experimental units. At the same time, the research question at hand may imply a focus on specified sets of two-factor interactions, while it is not justified to assume negligibility of other low order effects. An algorithm is provided for blocking a regular fraction into – possibly small – blocks while keeping specified two-factor interactions clear from confounding with main effects or other two-factor interactions. The proposed algorithm is implemented in the R package FrF2 and combines an estimability algorithm by the author with an automated implementation of a recent proposal for blocking fractions by hand.

中文翻译：

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一种用于阻止具有明确二因子交互作用的规则部分因子 2 水平设计的算法

摘要 具有 2 水平因子的规则部分因子设计是最常用的实验计划之一。在许多情况下，应该阻止设计以处理实验单元的不均匀性。同时，手头的研究问题可能意味着关注特定的双因素相互作用集，而假设其他低阶效应可以忽略不计是不合理的。提供了一种算法，用于将常规分数分成（可能是小）块，同时保持指定的双因素交互作用与主效应或其他双因素交互作用相混淆。所提出的算法在 R 包 FrF2 中实现，并将作者的可估计性算法与最近手动分块分数的建议的自动实现相结合。