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The purpose of this paper is to study the issue of employing the uniformity criterion measured by the mixture discrepancy to assess the optimal foldover plans for q-level factorials. The average mixture discrepancy and the average projection mixture discrepancy based on the level permutation method are respectively defined for combined designs, and the optimal foldover plan in terms of the overall uniformity and the uniformity of each dimension are also explored. The tight lower bounds of the average mixture discrepancy and the uniformity pattern under the general foldover plan are obtained respectively, which can be used as a benchmark for searching optimal foldover plans. Some illustrative examples are provided to show the theoretical results. [ABSTRACT FROM AUTHOR]

The issue of the projection uniformity of mixed two- and three-level factorials measured by mixture discrepancy is investigated in this paper. The average projection mixture discrepancy is defined to measure the uniformity for low-dimensions projection designs. Moreover, the relationship between uniformity pattern and generalized minimum aberration is established. Two numerical examples are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The objective of this paper is to discuss the issue of the projection uniformity of factorial designs measured by mixture discrepancy. The average projection discrepancy of combinatorially isomorphic designs obtained by level permutation on each factor is defined, which measures the projection uniformity on different dimensions. The uniformity pattern and minimum projection uniformity criterion for selecting optimal design are defined for q-level designs. The relationships between uniformity pattern, orthogonality and generalized word-length pattern are built. Moreover, a tight lower bound of uniformity pattern is also obtained. [ABSTRACT FROM AUTHOR]