Efficient Large Fractional Factorial Designs: Theory and Construction

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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.