An active interaction in a main effect plan may cause biased estimation of the parameters in an analysis of variance (ANOVA) model. A fractional factorial design (FFD) with higher order resolution can resolve the alias problem, however, with a considerable number of runs. Alternatively, a search design (SD), the so‐called main effect plus k plan (MEP.k), with much less number of runs than FFD, is able to search for k possible active interactions and estimate them in addition to estimating the main effects. However, the existing MEP.k's for 3^m factorial experiments are either proposed for a large m (e.g. m≥13) or have a large number of runs. In this paper, we proposed an irregular design for 3^m factorial experiments, which is able to identify the active two‐factor interactions and estimate them along with estimating the general mean and main effects for 3≤m≤14. The obtained design has fewer runs than the previous designs; meanwhile, it is also comparable and competitive in the discrimination and estimation performances with them. By simulation studies, it is shown that the proposed design does well in model identification and variable selection.

中文翻译：

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小行程设计，用于3m析因实验中的模型识别

主效果计划中的主动交互可能会导致方差分析（ANOVA）模型中的参数偏差估计。但是，具有较高阶分辨率的分数阶乘设计（FFD）可以解决混叠问题，但是需要进行大量的运行。可替换地，搜索设计（SD），即所谓的主效应加上ķ计划（MEP。ķ），与运行比FFD的少得多的数量，是能够搜索ķ可能的活性相互作用并估计它们在除了估计主要作用。但是，现有的环境保护部。ķ的为3^米阶乘实验要么提出用于大米（例如米≥13）或有大量运行。在本文中，我们提出了一个不规则设计为3^米阶乘实验，其能够鉴定活性双因素相互作用和估计它们与估计为3的一般性均值和主效应沿着≤米≤ 14将所得到的设计具有较少的比以前的设计运行；同时，它们在判别和估计性能上也具有可比性和竞争力。通过仿真研究表明，所提出的设计在模型识别和变量选择方面表现良好。