摘要
折叠是构造部分因析设计中的一种有效技术,能够有效解除因子效应的混杂,在许多文献中将这种增加第二个部分的设计称为折叠设计.使用可卷型L 2-偏差作为测量设计均匀性的准则,进一步研究二三混水平设计的最优折叠方案.基于水平置换的方法定义了一种新的折叠策略,极大地扩大了整个折叠空间,得到了所定义折叠方案的一些理论性质,并给出了组合设计可卷型L 2-偏差的一个更紧的下界,可作为搜索最优折叠方案的基准.
The foldover is a useful technique in construction of factorial designs,which can effectively eliminate the aliasing of factor effects.In many literatures,the design adding a second fraction is called a foldover design.In this paper,uniformity criterion measured by the wrap-around L 2-discrepancy is used to further study the optimal foldover plans for mixed two-and three-level designs.For mixed two-and three-level fractional factorials as the original designs,a new foldover strategy is provided based on level permutation of each factor,which vastly enlarge the full foldover space.Some theoretical properties of the defined foldover plans are obtained,a tighter lower bound of the wrap-around L 2-discrepancy of combined designs is also provided,which can be used as a benchmark for searching optimal foldover plans.
作者
罗彪
李洪毅
王治清
欧祖军
LUO Biao;LI Hong-yi;WANG Zhi-qing;OU Zu-jun(College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan,China)
出处
《兰州文理学院学报（自然科学版）》
2021年第2期20-25,共6页
Journal of Lanzhou University of Arts and Science(Natural Sciences)
基金
国家自然科学基金项目(11961027、11561025、11701213)
湖南省自然科学基金项目(2020JJ4497)
湖南省教育厅重点项目(18A284、19A403)
吉首大学研究生科研创新项目(JGY201931)。
关键词
最优折叠方案
水平置换
可卷型L
2-偏差
下界
optimal foldover
plan
level permutation
wrap-around L 2-discrepancy
lower bound
