定量因子析因设计的几何同构与最小象差
Geometric isomorphism and minimum aberration for factorial designs with quantitative factors
摘要：
析因设计在农业、工程和科学研究中有着广泛的应用。传统的设计理论在构造析因设计和研究析因设计的性质时，把所有的因子都看作是名义因子。然而，这不适合涉及定量因素的实验。对于具有定量因子的设计，设计矩阵中的一个或多个因子的水平置换可能导致不同的几何结构，并且因此导致不同的设计属性。本文引入指示函数来表示析因设计。一个多项式形式的指示函数被用来表征这些设计的几何结构。定义了几何同构，用于定量因素设计的分类。基于指示函数，提出了一种新的像差准则，并给出了一些最小像差设计。
英文摘要：
Factorial designs have broad applications in agricultural, engineering and scientific studies. In constructing and studying properties of factorial designs, traditional design theory treats all factors as nominal. However, this is not appropriate for experiments that involve quantitative factors. For designs with quantitative factors, level permutation of one or more factors in a design matrix could result in different geometric structures, and, thus, different design properties. In this paper indicator functions are introduced to represent factorial designs. A polynomial form of indicator functions is used to characterize the geometric structure of those designs. Geometric isomorphism is defined for classifying designs with quantitative factors. Based on indicator functions, a new aberration criteria is proposed and some minimum aberration designs are presented.
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