一般最小低阶混杂设计中混杂结构的研究与应用

项目名称： 一般最小低阶混杂设计中混杂结构的研究与应用

项目编号： No.11426161

项目类型： 专项基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 周琦

作者单位： 天津财经大学

项目金额： 3万元

中文摘要： 作为统计学的一个重要分支，试验设计在理论研究和实际应用中都有着重要意义，因子分析设计又是其中最为基础的部分。已有多种用于选取最优因子分析设计的最优准则被提出，并得到广泛应用。为了深入研究因子分析设计中的一些问题，一般最小低阶混杂(GMC)准则和设计被提出。随着该领域研究和应用工作的展开，GMC设计混杂结构的特性在其中起着重要的作用。本项目将主要关注GMC设计中混杂结构的研究与应用这一课题。首先，我们系统的描述和研究已构造的GMC设计的混杂结构，主要是提出别名集分类的概念，完善了二水平正规部分因子分析设计中的分类体系，在此基础上研究这些设计混杂结构的特性，给出相应的理论结果。其次，我们期望应用这些结果，给出一部分GMC设计和分区组GMC设计理论上的构造结果，以供实际使用。

中文关键词： 部分因子设计；分区组设计；正规设计；最优设计；

英文摘要： As one of the most important branches of statistics, design of experiments has important theoretical and practical significance, and factorial design is one of its foundational parts. To optimally select factorial designs, a few optimal criteria have been proposed and widely applied. To study the properties of factorial designs thoroughly, general minimum lower-order confounding (GMC) criterion and designs have been proposed. The characteristics of the confounding structures of these designs are essential to the research and applications in this field. This project will mainly focus on the research and applications of the confounding structures of GMC designs. At first, we systematically describe and study the confounding structures of constructed GMC designs, that is, we mainly propose the concept of classification of the aliased sets to complete the classified system in two-level regular fractional factorial designs. By studying their characteristics of the confounding structures, we provide a theoretical approach to obtain their confounding information. Based on these results, we expect to theoretically construct some GMC and blocked GMC designs, for practical use.

英文关键词： fractional factorial design；blocked design；regular design；Optimal Design；