非正规设计几个问题的深入研究

Nonregular design is a very important issue in design theory and received much attention for its flexibility of run size. But theory of nonregular design is not as crystal as that of regular design. This project will be based on the work of Ren (2007) and Ren (2012), by cooperation of members from different scientific branches, to give further study on nonregular designs with both aliasing and partial aliasing existed. It will include the problems of mathematical describing of nonregular factorial designs, confounding structure of asymmetric nonregualr design, confounding structure of nonregualr designs with more than one group of factors, date analysis method and optimal criteria under the strategy of using alias set as its core concept. Beside ordinary ways of study, the project is going to emphasize the use of combinatorial algebra and theory of differential equation as its tools and through the ways of cooperation among members of different backgrounds to handle complex problems. The success of this project will greatly promote the research and application of nonregular design theory and effectively enrich the theoretical system for design of experiment.

因为非正规设计在试验次数上更自由，是试验设计理论中的一个非常重要且广受关注的问题。然而关于非正规设计的理论和应用远不及正规设计透彻，本项目以Ren(2007)和Ren(2012)为研究基础，拟通过多学科的合作，对同时具有全别名和部分别名的非正规因析设计展开研究。内容包括非正规设计的描述问题；对非对称的非正规设计的混杂结构的研究；具有多组因子的非正规设计的混杂结构；在Ren(2012)以别名集为中心的分析策略下关于数据分析和优选法则的研究。除常规方法，本项目拟加强使用组合代数及微分方程作为工具，在多学科人员的合作下探讨解决复杂问题的新途径。本项目的顺利开展将对非正规设计的理论研究和实际应用起到极大的推进作用，能有效地丰富试验设计的理论体系。

本项目按照立项的申报内容展开了研究工作，主要是基于项目负责人前期的有关非正规混杂结构的结果展开在二水平非正规设计理论的若干方面进行研究。在对非正规设计的优选准则展开研究并得到一个最小G3-混杂优选准则；对因子分成二组以上的情况的非正规设计的混杂描述问题展开研究，得到一些阶段性理论结果，为该复杂混杂的描述给出前期理论基础；本项目还对非正规设计的均匀性与深度函数的关系进行探讨性性研究，拓展了解决这一问题的新途径。本项目成果包括一部学术专著，三篇期刊论文，并培养了若干名研究生及组建了研究团队。