A Class of Three-Level Designs for Definitive Screening in the Presence of Second-Order Effects
A Class of Three-Level Designs for Definitive Screening in the Presence of Second-Order Effects
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DOI：
10.1080/00224065.2011.11917841
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发表时间：
2011-01
影响因子：
2.5
通讯作者：
B. Jones;C. Nachtsheim
中科院分区：
文献类型：
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作者：
B. Jones;C. Nachtsheim
筛选设计对于评估大量因素对感兴趣的响应的相对影响是有吸引力的。实验者通常更喜欢三水平的定量因子而不是两水平因子，因为三水平允许对因子-响应关系中的曲率进行一些评估。然而，最熟悉的筛选设计将每个因素限制在两个水平。我们提出了一类新的设计，该设计具有三个水平，提供对任何二阶效应无偏的主效应估计值，只需要一次试验，试验次数是因子的两倍多，并且避免任何二阶效应对的混杂。此外，对于具有六个或更多因子的设计，我们的设计允许在任何三个因子中有效地估计完整的二次模型。在这方面，我们的设计可以使后续的实验在许多情况下是不必要的，从而提高整个实验过程的效率。我们还提供了一个算法的设计建设。
Screening designs are attractive for assessing the relative impact of a large number of factors on a response of interest. Experimenters often prefer quantitative factors with three levels over two-level factors because having three levels allows for some assessment of curvature in the factor—response relationship. Yet, the most familiar screening designs limit each factor to only two levels. We propose a new class of designs that have three levels, provide estimates of main effects that are unbiased by any second-order effect, require only one more than twice as many runs as there are factors, and avoid confounding of any pair of second-order effects. Moreover, for designs having six factors or more, our designs allow for the efficient estimation of the full quadratic model in any three factors. In this respect, our designs may render follow-up experiments unnecessary in many situations, thereby increasing the efficiency of the entire experimentation process. We also provide an algorithm for design construction.