Geometric isomorphism and minimum aberration for factorial designs with quantitative factors

By Shao-Wei Cheng, Kenny Q. Ye. 2004

152 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/496253a7f384b5ac335e63881d7838a43d345d4c

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In Computational Theory and Mathematics

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Citations in the corpus

Connections Among Different Criteria for Asymmetrical Fractional Factorial Designs (2006, background): “Refer to Cheng and Ye (2004) for criteria developed especially for quantitative factors. Each criterion mentioned above has its own merits. A natural question now arises: what connections or equivalencies exist among those criteria? This article aims to study the question for criteria for asymmetric”
Indicator function and complex coding for mixed fractional factorial designs (2007, methodology): “The representation of a fraction by its indicator polynomial function was generalized to designs with replicates in Ye (2003) and extended to not binary factors using orthogonal polynomials with an integer coding of levels in Cheng and Ye (2004) .”