Some Results On Fractional Factorial Design And Block Designs With Simple Structure

Recently, Zhang, Li, Zhao and Ai (2008) proposed a general minimum lower-order confounding (GMC for short) theory and a GMC criterion for choosing optimal fractional factorial designs. It is proved that, the GMC theory can manage the existing criteria for selecting designs. When an experiment has prior on important order of the factors, the GMC design is the best choice compared with any other optimal ones. Zhang, Wei and Li (2010) proposed a B-GMC criterion for choosing optimal blocking for two-level rgular designs. In this paper, we first prove some results on two-level fractional factoral design, and compare GMC criterion with MA criterion. Finally, we give the method of compare two block designs with simple structure.