Construction of main effects plans orthogonal through the block factor based on level permutation

Abstract

a b s t r a c tIn this paper, We first demonstrate that the orthogonal property of main effects plans orthogonal through the block factor (Bagchi, 2010) remains unchanged under level permutation. However, level permutation of factors could alter their geometrical structures and statistical properties. Hence uniformity is used to further distinguish main effects plans orthogonal through the block factor (POTB). A modified optimization algorithm is proposed to search uniform or nearly uniform POTBs and many new optimal POTBs with lowerdiscrepancy are obtained.

Construction of main-effect plans orthogonal through the block factor

“…Thus, uniformity or space-filling property (Fang et al, 2006;Yang et al, 2010;Ai et al, 2014;Tang et al, 2012;Zhou and Xu, 2014) via level permutation can be used to further distinguish different POTBs. Some progress in this direction is made in Chen et al (2015). …”