混料试验的格点填充设计  

Lattice Filling Design of Mixture Experiments of Mixture Experiments

作　　者：李光辉[1] 朱志彬 李俊鹏 张崇岐 LI GUANGHUI;ZHU ZHIBIN;LI JUNPENG;ZHANG CHONGQI(School of Science,Kaili University,Kaili 556011,China;Undergraduate School of Medical Business,Guangdong Pharmaceutical University,Guangzhou 510006,China;School of Economics and Statistics,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]凯里学院理学院,凯里556011 [2]广东药科大学医药商学院,广州510006 [3]广州大学经济与统计学院,广州510006

出　　处：《应用数学学报》2022年第4期607-623,共17页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(12071096);国家自然科学基金青年项目(11901260);贵州省科学技术基金(黔科合基础[2020]1Y010);广东省中医药局科研项目(20201198);凯里学院博士专项课题(BS201807)资助.

摘　　要：格子点集填充方法是基于空间填充设计的思想构造试验域内均匀分布设计点的首选方法格子点集所引出的空间填充设计方法在超立方体上有很多好的性质,有许多出色的工作对此做了研究和总结.混料试验域比超立方体的情况更复杂且目前研究成果较少,本文通过构造混料试验的格点填充设计,使得均方误偏差与最大距离偏差有显式表达.这里首先给出了混料试验域的剖分方法,然后讨论了混料格点填充及其性质,其次构造了单纯形的保距独立变换与正交性的格点填充设计,给出例子说明方法的有效性.最后提出了可进一步研究的问题.The lattice point set filling method is the first choice to construct the uniform distribution design points in an experimental region based on the idea of space filling design.The space filling design met hod derived from the lattice point set has many good properties in the hypercube.A lot of excellent works have been done in this field.The experimental region of mixture has more complex environment than hypercube,and related works are rarely found.In this paper,we obtain the expression of mean square error discrepancy and maximum distance discrepancy by constructing the lattice filling design of mixture region.Firstly,the division method of mixture region is given along with the discussion of the lattice filling of mixture experimen ts and its properties.Then,we construet the lattice filling design distance that preserving independen11ransformation and orthogonal properties,and propose examples to show the effectiveness of our method.At last,some further problems are put forward.

关 键 词：格子点集 单纯形 偏差 

分 类 号：O212.7[理学—概率论与数理统计]