Efficient Large Fractional Factorial Designs: Theory and Construction

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

Fractional factorial designs are among the most widely used experimental plans in practice. Most existing researches are limited to small fractional factorial designs. The objectives of this proposed research are to develop a general theory and to construct efficient large fractional factorial designs for practical use. The concept of moment projection pattern is introduced to study design isomorphism. Linear programming technique is used to study design optimality. Efficient algorithms are proposed for constructing both regular and nonregular designs. The concept of minimum moment aberration is utilized to study optimal blocking schemes for both regular and nonregular designs. Coding theory is employed to develop a general theory on minimum aberration blocking schemes. Catalogs of efficient large fractional factorial designs are built for practical use. Experimental design is an effective and commonly used tool in scientific investigation. Fractional factorial designs are among the most widely used experimental plans in practice. Most existing researches are limited to small fractional factorial designs. Progresses in science and technology urge the study of efficient fractional factorial designs with both large run sizes and a large number of factors. Some recent examples are computer experiments in large scale simulation, high throughput screening in drug discovery, and microarray experiments in biotechnology. The objectives of this proposed research are to develop a general theory and to construct efficient large fractional factorial designs for practical use. Addressing the fundamental issue of design construction and selection, the results of the proposed research can be quickly assimilated into graduate courses on experimental design. New algorithms and efficient designs will be made available online for broad and quick dissemination. The proposed research has wide-ranging impact both theoretically and practically, and will lead to remarkable new advances in design theory and better practice in experimentation.