因析设计的一般最小低阶混杂构造理论及应用

Design of experiment has played a fundamental role in the statistical curriculum. It lays out a detailed experimental plan in advance of doing the experiment, and obtains the amount of essence information for solving the questions of interest as clearly and efficiently. Factorial designs are widely used in various experiments. Optimality theories and construction methods of designs are the core of investigation on experimental designs. They are very important in practice as well as theory, which have great economic effect and social benefit. .The purpose of this project is to extend genreal minimum lower-order (GMC) theory to higher-level designs such as regular designs, block designs and mixed-level designs. The main contents are as following: (1)Study properties and construction of three-level regular designs and block designs with GMC. (2)Analyze properties of S-level GMC criterion and construct S-level regualr and block GMC designs. (3)Study mixed-level GMC criterion. (4)Develop a set of calculation and application software for GMC designs.

试验设计是统计学的重要分支，主要研究如何设计试验从而获得事物本质信息的一项科学技术。因析设计在各类试验中应用十分广泛，其最优设计理论和构造方法是试验设计的核心内容，这不仅理论上需要，更重要的是高效的试验会带来巨大的经济效益。.本项目将对最优设计理论中的一般最小低阶混杂(General minimum lower-order confounding, 简记GMC)理论展开深入研究，将GMC理论推广到高水平情形，包括正规、分区组以及混水平等设计，主要研究内容为：(1)三水平的正规设计和区组设计GMC准则的性质和GMC设计的构造；(2)S水平的正规设计和区组设计GMC准则的性质与设计的构造；(3)混水平设计的GMC理论；以及(4)研究一套计算和应用GMC设计软件。

试验设计是统计学的重要分支，主要研究如何设计试验从而获得事物本质信息的一项科学 技术。因析设计在各类试验中应用十分广泛，其最优设计理论和构造方法是试验设计的核心内容，这不仅理论上需要，更重要的是高效的试验会带来巨大的经济效益。 本项目对最优设计理论中的一般最小低阶混杂(General minimum lower-order confoun ding, 简记GMC)理论展开深入研究，将GMC理论推广到高水平情形，包括正规、分区组以及混 水平等设计，完成主要内容为：(1) 三水平的正规设计和区组设计GMC准则的性质和GMC设计的构造；(2) S水平的GMC正规设计的性质与设计的构造；(3) 混水平设计的GMC理论；以及(4) 给出一套计算和应用GMC设计软件。