The objective of this paper is to study the issue of uniformity on three-level U-type designs in terms of the wrap-around L2-discrepancy.Based on the known formula,we present a new lower bound of wrap-around L2-discre...The objective of this paper is to study the issue of uniformity on three-level U-type designs in terms of the wrap-around L2-discrepancy.Based on the known formula,we present a new lower bound of wrap-around L2-discrepancy for three-level U-type designs and compare it with those existing ones through figures,numerical simulation and illustrative examples.展开更多
The purpose of the present article is to introduce a class of mixed two- and three-level extended designs obtained by adding some new runs to an existing mixed two- and three-level design. A formulation of wrap-around...The purpose of the present article is to introduce a class of mixed two- and three-level extended designs obtained by adding some new runs to an existing mixed two- and three-level design. A formulation of wrap-around L2-discrepancy for the extended designs is developed. As a benchmark of obtaining （nearly） uniform asymmetrical extended designs, a lower bound to the wrap-around L2- discrepancy for our proposed designs is established. Thorough numerical results are displayed, which provide further corroboration to the derived theoretical results.展开更多
基金Supported in part by the National Natural Science Foundation of China(Nos.11871237,11801576,11271147,11401596)the Fundamental Research Funds for the Central Universities(South-Central University for Nationalities(Nos.CZQ18017,CZQ19010))
文摘The objective of this paper is to study the issue of uniformity on three-level U-type designs in terms of the wrap-around L2-discrepancy.Based on the known formula,we present a new lower bound of wrap-around L2-discrepancy for three-level U-type designs and compare it with those existing ones through figures,numerical simulation and illustrative examples.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271147,11471135,11471136support of Excellent Doctoral Dissertation to Cultivate Project of Central China Normal University under Grant No.2017YBZZ057
文摘The purpose of the present article is to introduce a class of mixed two- and three-level extended designs obtained by adding some new runs to an existing mixed two- and three-level design. A formulation of wrap-around L2-discrepancy for the extended designs is developed. As a benchmark of obtaining （nearly） uniform asymmetrical extended designs, a lower bound to the wrap-around L2- discrepancy for our proposed designs is established. Thorough numerical results are displayed, which provide further corroboration to the derived theoretical results.
