基于均匀性的部分因析设计最优折叠反转及相关问题的研究与应用

Design of experiment is an important branch of statistics, and it plays an improving role for the development of agriculture and industry, economics, biomedical, social science, and so on. As an important method of fractional factorial design and computer experiment, uniform design has been used extensively in practice. The aliasing of factorial effects is an inevitable consequence of using fractional factorial design. As a classical and effective method to break the aliasing, foldover has been universally acknowledged and applied since the method is proposed in the 1960s. However, there are many basic issues deserve to systematically research. On the basis of the existing works, this project aims to study the optimal foldover plans of fractional factorial design and related issues based on uniformity criterion. Firstly, the issues such as uniform foldover plans, semi-foldover plans and simultaneously blocking and semi-foldover plans of two-level designs will be investigated thoroughly. Second, the uniform foldover plans and their properties of multi-level, mixed-level fractional factorial will be studied, respectively. Third, some designs and computer experiments possessed excellent properties will be constructed via foldover technique and its idea. The objective of this project is to build up the general theory of optimal foldover plans of fractional factorial designs based on uniformity criterion, and construct some designs and computer experiments possessed excellent properties. These research results will enrich and improve the theory of factorial designs and uniform designs, and provide convenince and guidance for the practical application.

试验设计是统计学的重要分支之一，为工农业、经济、生物医药和社会科学等的发展起到了巨大的推动作用。均匀设计作为一种重要的部分因析设计和计算机试验方法在实际中得到了广泛应用。效应别名是部分因析设计中的重要问题，折叠反转作为解除别名效应的经典、有效的方法从上世纪60年代提出以来已获得公认和应用，但仍有许多基础问题需要深入研究。本项目将在已有的研究基础上，旨在基于均匀性准则对部分因析设计的最优折叠反转及相关问题开展研究：（一）深入研究两水平设计均匀的折叠反转、半折叠反转及同时分区组和半折叠反转等问题；（二）分别研究多水平、混水平部分因析设计的均匀折叠反转方案及性质；（三）利用折叠反转技术和思想构造具有优良性质的设计和计算机试验。本项目的目标是建立部分因析设计基于均匀性的最优折叠反转的一般理论，并构造一些优良设计和计算机试验，进一步丰富和完善因析设计、均匀设计的理论，为实际应用提供便利和指导。

效应别名是部分因析设计中的重要问题，折叠反转作为解除别名效应的经典、有效的方法从上世纪60 年代提出以来已获得公认和应用。本项目在已有的研究基础上，基于均匀性准则对部分因析设计的最优折叠反转及相关问题开展研究：（一）深入研究了两水平设计均匀的折叠反转问题，获得其组合设计的中心化L2-偏差更紧的下界；（二）分别研究了多水平、混水平部分因析设计的均匀折叠反转方案及性质，并在可卷型L2-偏差下讨论了其最优的折叠反转方案；（三）利用折叠反转、半折叠反转的技术和思想构造了具有优良性质的设计，如部分重复的因析设计、Sudoku设计及Sudoku-based均匀设计。本项目建立了部分因析设计基于均匀性的最优折叠反转的一般理论，并构造了一些优良设计，进一步丰富和完善因析设计、均匀设计的理论，为实际应用提供了便利和指导。.