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 ...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.展开更多
The theory of uniform design has received increasing interest because of its wide application in the field of computer experiments.The generalized discrete discrepancy is proposed to evaluate the uniformity of the mix...The theory of uniform design has received increasing interest because of its wide application in the field of computer experiments.The generalized discrete discrepancy is proposed to evaluate the uniformity of the mixed-level factorial design.In this paper,the authors give a lower bound of the generalized discrete discrepancy and provide some construction methods of optimal mixed-level uniform designs which can achieve this lower bound.These methods are all deterministic construction methods which can avoid the complexity of stochastic algorithms.Both saturated mixed-level uniform designs and supersaturated mixed-level uniform designs can be obtained with these methods.Moreover,the resulting designs are also χ^(2)-optimal and minimum moment aberration designs.展开更多
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）.
文摘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supported by the National Natural Science Foundation of China under Grant Nos.12131001,12226343,12371260,and 12371261National Ten Thousand Talents Program of Chinathe 111 Project under Grant No.B20016.
文摘The theory of uniform design has received increasing interest because of its wide application in the field of computer experiments.The generalized discrete discrepancy is proposed to evaluate the uniformity of the mixed-level factorial design.In this paper,the authors give a lower bound of the generalized discrete discrepancy and provide some construction methods of optimal mixed-level uniform designs which can achieve this lower bound.These methods are all deterministic construction methods which can avoid the complexity of stochastic algorithms.Both saturated mixed-level uniform designs and supersaturated mixed-level uniform designs can be obtained with these methods.Moreover,the resulting designs are also χ^(2)-optimal and minimum moment aberration designs.
