Studies in Fractional Factorial Design

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

This project is concerned with how to choose good fractional factorial designs. Minimum aberration is a well accepted optimality criterion for selecting the so called regular fractional factorial designs. Using results from finite projective geometry and coding theory, the investigator continues his work on the determination of minimum aberration designs, in particular, those of resolution IV. Resolution IV designs have nice structures and good statistical properties, but have not been well studied in the past, partly due to the lack of a good structural theory. Some recent results in finite projective geometry provide powerful tools for understanding the structures of resolution IV designs and for helping solve the problem of constructing optimal and efficient designs. The investigator also studies the construction of new orthogonal arrays of strength three, the nonregular counterpart of regular designs of resolution IV. Finally, the investigator addresses several issues of designing experiments that involve multiple processing stages, ranging from formulation of optimality criteria to theoretical and algorithmic construction of good designs. Statistical design of experiments is used in a wide range of scientific and industrial investigations. Experiments need to be properly designed so that valid information can be extracted at a lower cost. In industrial experiments, often a large number of factors have to be studied, but the experiments are expensive to conduct. In this case, only a small fraction of all the possible combinations of the factors can be observed, and how to choose a good fraction is an important issue. The study of such designs has received considerable attention, mainly due to the success in applications to experiments for improving quality and productivity in industrial manufacturing. This research is to study the construction of efficient designs to extract more information. Better industrial experiments can improve the quality of products and reduce production cost. Experimenters will be benefited by having a greater repertoire of new and good designs at their disposal, and will be able to run their experiments more efficiently. For example, one of the proposed activities is concerned with experiments with multiple processing stages which often arise in industrial applications such as the fabrication of integrated circuits.