Projection uniformity under mixture discrepancy

The objective of this paper is to discuss the issue of projection uniformity under mixture discrepancy (MD). The uniformity pattern (UP) and minimum projection uniformity criterion are defined for two- and three-level designs under MD. It is shown that the projection uniformity under MD is better than that of other discrepancies, and there is a linear relationship between UP and generalized word-length pattern. Moreover, it is also shown that the foldover technique can increase uniformity resolution. The lower bounds of projection discrepancy for foldover designs and more general follow-up designs are also obtained for two-level designs. For three-level designs, the UP is defined through the average projection discrepancy based on level permutation of factors and its property is also discussed.