混水平列扩充设计的混偏差的下界

数学物理学报 ›› 2021, Vol. 41 ›› Issue (3): 882-891.

混水平列扩充设计的混偏差的下界

雷轶菊¹(),欧祖军²(),赵国喜¹

¹ 新乡学院数学与统计学院河南新乡 453003
² 吉首大学数学与统计学院湖南吉首 416000

收稿日期:2019-12-30 出版日期:2021-06-26 发布日期:2021-06-09
作者简介:雷轶菊, E-mail: leiyiju2001@sina.com|欧祖军, E-mail: ozj9325@mail.ccnu.edu.cn
基金资助:
国家自然科学基金(11961027);国家自然科学基金(11701213);国家自然科学基金(11871237);国家自然科学基金(11561025);河南省高等学校重点科研项目(19A110032);湖南省教育厅重点科研项目(18A284);湖南省教育厅重点科研项目(19A403)

Lower Bounds on Mixture-Discrepancy of the Mixed-Level Column Augmented Design

Yiju Lei¹(),Zujun Ou²(),Guoxi Zhao¹

¹ College of Mathematics and Statistics, Xinxiang University, Henan xinxiang 453003
² College of Mathematics and Statistics, Jishou University, Hunan Jishou 416000

Received:2019-12-30 Online:2021-06-26 Published:2021-06-09
Supported by:
the NSFC(11961027);the NSFC(11701213);the NSFC(11871237);the NSFC(11561025);the Key Scientific Research Project of Henan Colleges and Universities(19A110032);the Key Scientific Research Project of Education Department of Hunan Province(18A284);the Key Scientific Research Project of Education Department of Hunan Province(19A403)

摘要/Abstract

摘要：

扩充设计作为一种新型的试验设计，近年来受到学者越来越广泛地关注.扩充设计包括初始设计与跟随设计两部分.在许多跟随设计中，在跟随阶段可以加入一些另外的2-水平或3-水平因子，因为它们在初始阶段可能被忽略但又十分重要.该文在均匀性准则下，给出了列扩充设计在混偏差下的解析表达式及相应的下界，列举了混偏差意义下的混水平列扩充近似均匀设计.

关键词: 跟随设计, 混偏差, 下界

Abstract:

As a new type of experimental designs, the extended designs have been paid more and more attention in recent years. The extended design includes two parts: initial design and follow-up design. In many follow-up designs, some extra factors with two or three levels may be added in the follow-up stage since they are quite important but may be neglected in the initial stage. In this paper, under the uniformity criterion, we present the analytical expressions and the corresponding lower bounds on mixture-discrepancy of the mixed-level column augmented designs. In the sense of mixed discrepancy, mixed-level column augmented nearly uniform designs are proposed.

Key words: Follow-up design, Mixture-discrepancy, Lower bound

中图分类号:

O212.6

雷轶菊,欧祖军,赵国喜. 混水平列扩充设计的混偏差的下界[J]. 数学物理学报, 2021, 41(3): 882-891.

Yiju Lei,Zujun Ou,Guoxi Zhao. Lower Bounds on Mixture-Discrepancy of the Mixed-Level Column Augmented Design[J]. Acta mathematica scientia,Series A, 2021, 41(3): 882-891.

图/表 2

参考文献 15

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n₁	m₁	m₂	r
2\|n₁		m₂=0	r≥0
3\|n₁	m₁=0		r=0
6\|n₁	m₁=0		r>0
	m₁>0	m₂>0	r₀

n₁	r	[MD(D₃)]²	LBM₁	Eff	d₂
6	1	651.2708	630.2081	0.9677	1	12	122	2111	21221	222111
6	2	1.19E+03	1.15E+03	0.9707	2	21	112	1221	11212	111212
6	3	2.15E+03	2.09E+03	0.9728	2	11	221	1222	12121	122112
6	4	3.91E+03	3.82E+03	0.9771	2	22	221	2111	12221	212221
6	5	6.96E+03	6.83E+03	0.9810	1	12	111	1222	22112	211221
6	6	1.24E+04	1.22E+04	0.9859	1	21	212	2112	21112	121122

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