Uniform two-dimensional projection designs with mixed two-and three-levels

Mixed two- and three-level designs are widely used in both computer experiments and physical experiments. According to the effect hierarchy principle of factors, the lower-order effect is more important than the higher-order case, especially the main effect of factors. This paper primarily focuses on the two-dimensional projection uniformity of mixed two- and three-level designs. Firstly, a measure of two-dimensional projection uniformity is defined for asymmetric designs. Secondly, the analytical connection is established between this measure and the centralized L1-distance for mixed two- and three-level designs, and a tight lower bound of the measure is derived, serving as a benchmark for evaluating two-dimensional projection uniformity of designs and searching for uniform two-dimensional projection designs. Thirdly, the analytical connection is established between the correlation coefficient and the L2-distance of mixed two- and three-level designs is provided. Finally, the application of a uniform two-dimensional projection design in OTC push-pull circuits is provided for explaining its excellent performance.