Uniformity of Asymmetric Augmented Designs  

作　　者：Zhi-qing WANG Xiang-yu FANG Zu-jun OU 

机构地区：[1]College of Mathematics and Statistics,Jishou University,Jishou 416000,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第4期1025-1044,共20页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.12361053,11961027,12161040);Hunan Provincial Natural Science Foundation of China(No.2023JJ30486);Scientific Research Plan Item of Hunan Provincial Department of Education(No.22A0355)。

摘　　要：Follow-up experimental designs are widely applied to explore the relationship between factors and responses step by step in various fields such as science and engineering.When some additional resources or information become available after the initial design of experiment is carried out,some additional runs and/or factors may be added in the follow-up stage.In this paper,the issue of the uniform row augmented designs and column augmented designs with mixed two-,three-and four-level is investigated.The uniformity of augmented designs is discussed under the wrap-around L_(2)-discrepancy.Some lower bounds of wrap-around L_(2)-discrepancy for the augmented designs are obtained,which can be used to assess uniformity of augmented design.Numerical results show that augmented designs have high efficiency,which have low discrepancy and close to the proposed lower bounds.

关 键 词：augmented design follow-up design uniform design wrap-around L_(2)-discrepancy 

分 类 号：O212.6[理学—概率论与数理统计]