Application Of Minimum Projection Uniformity In Complementary Designs

There are many criterions to assess and compare two-level factorials. For example, minimum aberration criterion, generalized minimum aberration criterion, orthogonal criterion, V-criterion, and so on. Recently, based on a so-called uniformity pattern, Fang and Qin (2004) proposed the minimum projection uniformity criterion to compare two level factorials. They also studied the statistical rationality of this criterion. Zhang and Qin (2006) gave applications of minimum projection uniformity criterion in fractional factorial designs, such as in aberration designs, orthogonal arrays, supersaturated designs, etc. In present paper, we continue this study, and focus on the application of minimum projection uniformity criterion in complementary designs. We call D and D are a pair of complementary designs, if D = (D:D) is a U-type design and all the Hamming distances of any two runs are the same. An analysis relationship between the uniformity pattern I_i(D) and I_i(D) of a pair of complementary designs D and D is established. Based on this analysis relationship, we propose the MPU rule, which can be used to compare two-level factorials. And two applications are given to illustrate our conclusions.