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CONFOUNDING STRUCTURE OF TWO-LEVEL NONREGULAR FACTORIAL DESIGNS

Acta Mathematica Scientia 2012年第2期32卷 488-498页

作者：任俊柏 School of Statistics Jiangxi University of Finance and Economics

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.

关键词： Nonregular design alias set partial aliasing

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Matrix Image Method for Ranking Nonregular Fractional Factorial Designs

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Acta Mathematicae Applicatae Sinica 2018年第4期34卷 742-751页

作者： Xue-ping CHEN Jin-guan LIN Xuan-qing CHEN Xiao-di WANG Department of Statistics Jiangsu University of Technology Changzhou 213001 China Department of Statistics Nanjing Audit University Nanjing 211815 China School of Statistics and Mathematics Central University of Finance and Economics Beijing 100081 China

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.

关键词： generalized minimum aberration Bayes matrix image partial aliasing

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