摘要
We study the complementary design problem, which is to express the uniformity pattern of a q-level design in terms of that of its complementary design. Here, a pair of complementary designs form a design in which all the Hamming distances of any two distinct runs are the same, and the uniformity pattern proposed by H. Qin, Z. Wang, and K. Chatterjee [J. Statist. Plann. Inference, 2012, 142： 1170-11771 comes from discrete discrepancy for q-level designs. Based on relationships of the uniformity pattern between a pair of complementary designs, we propose a minimum projection uniformity rule to assess and compare q-level factorials.
We study the complementary design problem, which is to express the uniformity pattern of a q-level design in terms of that of its complementary design. Here, a pair of complementary designs form a design in which all the Hamming distances of any two distinct runs are the same, and the uniformity pattern proposed by H. Qin, Z. Wang, and K. Chatterjee [J. Statist. Plann. Inference, 2012, 142： 1170-11771 comes from discrete discrepancy for q-level designs. Based on relationships of the uniformity pattern between a pair of complementary designs, we propose a minimum projection uniformity rule to assess and compare q-level factorials.
基金
Acknowledgements The authors greatly appreciate helpful suggestions of the referees that greatly improved the paper. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11271147, 11401596）.
