Efficient Large Fractional Factorial Designs: Theory and Construction

部分析因设计是实践中应用最广泛的实验方案之一。现有的研究大多局限于小分数析因设计。这项研究的目标是发展一个普遍的理论，并为实际使用构建有效的大部分析因设计。为了研究设计同构，引入了矩投影模式的概念。利用线性规划技术对设计优化问题进行了研究。提出了构造正则设计和非正则设计的有效算法。利用最小矩像差的概念，研究了规则设计和非规则设计的最优分块方案。利用编码理论发展了最小像差遮挡方案的一般理论。实验设计是科学研究中一种有效而常用的工具。部分析因设计是实践中应用最广泛的实验方案之一。现有的研究大多局限于小部分析因设计。科学技术的进步促使对既有较大规模又有较多因素的有效部分析因设计的研究。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。这项研究的目的是发展一种普遍的理论，并为实际应用构造有效的大部分析因设计。针对设计构建和选择的基本问题，建议的研究结果可以很快被吸收到实验设计的研究生课程中。新的算法和高效的设计将在网上提供，以便广泛和快速地传播。本文的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取得显著的新进展。

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.