Efficient Large Fractional Factorial Designs: Theory and Construction

部分因子设计是实践中应用最广泛的试验方案之一。 现有的研究大多局限于小析因设计。本研究的目的是建立一个通用的理论，并构造有效的大部分因子设计用于实际应用。 引入矩投影模式的概念来研究设计同构。用线性规划技术研究设计的最优性。提出了构造正则和非正则设计的有效算法。 利用最小矩象差的概念研究了正则和非正则设计的最优区组方案。 本文应用编码理论，建立了最小像差阻塞方案的一般理论。实验设计是科学研究中常用的有效工具。部分因子设计是实践中应用最广泛的试验方案之一。 现有的研究大多局限于小析因设计。科学技术的进步促使人们研究大规模、多因子的有效部分析因设计。最近的一些例子是大规模模拟中的计算机实验，药物发现中的高通量筛选，以及生物技术中的微阵列实验。 本研究的目的是建立一个通用的理论，并构造有效的大部分析因设计以供实际应用。解决了设计构建和选择的基本问题，所提出的研究结果可以很快地被吸收到实验设计的研究生课程中。 新的算法和有效的设计将在网上广泛而快速地传播。 该研究具有广泛的理论和实践意义，将在设计理论和实验实践方面带来显著的新进展。

Fractional factorial designs are among the most widely used experimentalplans in practice. Most existing researches are limited to smallfractional factorial designs. The objectives of this proposed research areto develop a general theory and to construct efficient large fractionalfactorial designs for practical use. The concept of moment projectionpattern is introduced to study design isomorphism. Linear programmingtechnique is used to study design optimality. Efficient algorithms areproposed for constructing both regular and nonregular designs. Theconcept of minimum moment aberration is utilized to study optimal blockingschemes for both regular and nonregular designs. Coding theory isemployed to develop a general theory on minimum aberration blockingschemes. Catalogs of efficient large fractional factorial designs arebuilt for practical use.Experimental design is an effective and commonly used tool in scientificinvestigation. Fractional factorial designs are among the most widely usedexperimental plans in practice. Most existing researches are limited tosmall fractional factorial designs. Progresses in science and technologyurge the study of efficient fractional factorial designs with both largerun sizes and a large number of factors. Some recent examples are computerexperiments in large scale simulation, high throughput screening in drugdiscovery, and microarray experiments in biotechnology. The objectives ofthis proposed research are to develop a general theory and to constructefficient large fractional factorial designs for practical use. Addressing the fundamental issue of design construction and selection, theresults of the proposed research can be quickly assimilated into graduatecourses on experimental design. New algorithms and efficient designs willbe made available online for broad and quick dissemination. The proposedresearch has wide-ranging impact both theoretically and practically, andwill lead to remarkable new advances in design theory and better practicein experimentation.