In design theory, the alias structure of regular fractional factorial designs is elegantly described with group theory. However, this approach cannot be applied to nonregular designs directly. For an arbitrary nonregu...In design theory, the alias structure of regular fractional factorial designs is elegantly described with group theory. However, this approach cannot be applied to nonregular designs directly. For an arbitrary nonregular design, a natural question is how to describe the confounding relations between its effects, is there any inner structure similar to regular designs？ The aim of this article is to answer this basic question. Using coefficients of indicator function, confounding structure of nonregular fractional factorial designs is obtained as linear constrains on the values of effects. A method to estimate the sparse significant effects in an arbitrary nonregular design is given through an example.展开更多
Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. In this paper,we study m...Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. In this paper,we study matrix image theory and present a new method for distinguishing and assessing nonregular designs with complex alias structure, which works for all symmetrical and asymmetrical, regular and nonregular orthogonal arrays. Based on the matrix image theory, our proposed method captures orthogonality and projection properties. Empirical studies show that the proposed method has a more precise differentiation capacity when comparing with some other criteria.展开更多
基金supported by the NNSF of China grant 71161013the MOE Project of Humanities and Social Sciences No.10YGC630203
文摘In design theory, the alias structure of regular fractional factorial designs is elegantly described with group theory. However, this approach cannot be applied to nonregular designs directly. For an arbitrary nonregular design, a natural question is how to describe the confounding relations between its effects, is there any inner structure similar to regular designs？ The aim of this article is to answer this basic question. Using coefficients of indicator function, confounding structure of nonregular fractional factorial designs is obtained as linear constrains on the values of effects. A method to estimate the sparse significant effects in an arbitrary nonregular design is given through an example.
基金supported by National Natural Science Foundation of China(Nos.11601195,11601538,11571073)Natural Science Foundation of Jiangsu Province of China(No.BK20160289)+1 种基金Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.16KJB110005)Jiangsu Qing Lan Project
文摘Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. In this paper,we study matrix image theory and present a new method for distinguishing and assessing nonregular designs with complex alias structure, which works for all symmetrical and asymmetrical, regular and nonregular orthogonal arrays. Based on the matrix image theory, our proposed method captures orthogonality and projection properties. Empirical studies show that the proposed method has a more precise differentiation capacity when comparing with some other criteria.
