Construction Of Regular Designs For Large Number Of Factor

For regular fractional factorial designs, Zhang, Li, Zhao and Ai (2008) introduced a new classification pattern, called aliased effect number pattern (AENP). Based on the AENP, they proposed a general minimum lower order confounding (GMC) criterion for selecting optimal designs. Zhang, Li and Zhao (2010), Zhang and Cheng (2010) and Cheng and Zhang (2010) developed the theories of constructing GMC 2 n(?)m designs respectively for parameter intervals 5 N /16+ 1≤n≤N(?)1, 33 N /128+ 1≤n≤5N/16and N / 4+ 1≤n≤9N/32and obtained all the GMC designs for these parameters, where N= 2n (?)m and n are respectively runs and the number of factors.We have noted that, when the number of factors is large, even for GMC designs which have general minimum lower order confounding, their lower order effects are severely confounding with each other. So, we can image that, for any two designs both of which have large number of factors, they will do not have a significant difference. To confirm this guess, in this paper we investigate this problem theoretically and quantitatively. First we introduce a concept of similarity of two designs on their confounding, called as close coefficient, and then compare the GMC, MA and the worst design on the coefficient to find how much differences between them. We conclude that, if the number of factors is large enough, then all the designs chosen from the saturated design have only a slight difference on the confounding between the lower order effects. Therefore, we suggest that the GMC designs are always a suitable choice under any existing criteria, sine the GMC designs not only have the property of the general minimum lower order confounding and the simplest construction, but also it is very easy to do data analysis for them.This conclusion will help experimenters to enhance the experimental efficiency.