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The Scientific World Journal
Volume 2015, Article ID 163234, 9 pages
http://dx.doi.org/10.1155/2015/163234
Research Article

Results for Two-Level Designs with General Minimum Lower-Order Confounding

1School of Mathematical Sciences, Xinjiang University, Urumqi 830046, China
2KLAS and School of Mathematics, Northeast Normal University, Changchun 130024, China
3LPMC and School of Mathematical Sciences, Nankai University, Tianjin 300071, China

Received 2 June 2014; Accepted 19 November 2014

Academic Editor: Haijun Jiang

Copyright © 2015 Zhi Ming Li and Run Chu Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The general minimum lower-order confounding (GMC) criterion for two-level design not only reveals the confounding information of factor effects but also provides a good way to select the optimal design, which was proposed by Zhang et al. (2008). The criterion is based on the aliased effect-number pattern (AENP). Therefore, it is very important to study properties of AENP for two-level GMC design. According to the ordering of elements in the AENP, the confounding information between lower-order factor effects is more important than that of higher-order effects. For two-level GMC design, this paper mainly shows the interior principles to calculate the leading elements and in the AENP. Further, their mathematical formulations are obtained for every GMC design with according to two cases: (i) and (ii) .