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Building some bridges among various experimental designs
Journal of the Korean Statistical Society ( IF 0.6 ) Pub Date : 2020-01-01 , DOI: 10.1007/s42952-019-00004-0
A. M. Elsawah

Designing their experiments is the significant problem that experimenters face. Maximin distance designs, supersaturated designs, minimum aberration designs, uniform designs, minimum moment designs and orthogonal arrays are arguably the most exceedingly used designs for many real-life experiments. From different perspectives, several criteria have been proposed for constructing these designs for investigating quantitative or qualitative factors. Each of those criteria has its pros and cons and thus an optimal criterion does not exist, which may confuse investigators searching for a suitable criterion for their experiment. Some logical questions are now arising, such as are these designs consistent, can an optimal design via a specific criterion perform well based on another criterion and can an optimal design for screening quantitative factors be optimal for qualitative factors? Through theoretical justifications, this paper tries to answer these interesting questions by building some bridges among these designs. Some conditions under which these designs agree with each other are discussed. These bridges can be used to select a suitable criterion for studying some hard problems effectively, such as detection of (combinatorial/geometrical) non-isomorphism among designs and construction of optimal designs. Benchmarks for reducing the computational complexity are given.

中文翻译:

在各种实验设计之间架起桥梁

设计实验是实验人员面临的重大问题。Maximin距离设计,过饱和设计,最小像差设计,均匀设计,最小矩设计和正交阵列可以说是许多实际实验中使用最多的设计。从不同的角度来看,已经提出了一些标准来构建这些设计以研究定量或定性因素。这些标准中的每一个都有其优缺点,因此不存在最佳标准,这可能会使研究人员难以为其实验寻找合适的标准。现在出现了一些逻辑问题,例如这些设计是否一致,通过特定标准的最佳设计是否可以在另一个标准的基础上很好地发挥作用?用于筛选定量因素的最佳设计是否可以对定性因素进行优化?通过理论上的论证,本文试图通过在这些设计之间建立一些桥梁来回答这些有趣的问题。讨论了这些设计彼此一致的一些条件。这些桥梁可用于选择合适的准则,以有效地研究一些难题,例如检测设计之间的(组合/几何)非同构性和优化设计的构造。给出了降低计算复杂度的基准。讨论了这些设计彼此一致的一些条件。这些桥梁可用于选择合适的标准,以有效地研究一些难题,例如检测设计之间的(组合/几何)非同构性和构建最佳设计。给出了降低计算复杂度的基准。讨论了这些设计彼此一致的一些条件。这些桥梁可用于选择合适的标准,以有效地研究一些难题,例如检测设计之间的(组合/几何)非同构性和构建最佳设计。给出了降低计算复杂度的基准。
更新日期:2020-01-01
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