The investigator studies several problems in the theory of fractional factorial design. Some recent results in finite projective geometry provide powerful tools for characterizing the structures of regular fractional factorial designs of resolution IV in certain important cases. One major research activity is to expand these tools and apply them to develop a comprehensive theory for the determination and construction of optimal regular fractional factorial designs of resolution IV under the criterion of minimum aberration. The results are further extended to nonregular designs and the situation where the experimental units are divided into more homogeneous blocks to improve precision. The research on nonregular designs provides new methods for constructing orthogonal arrays of strength three. Hidden projection properties of multi-level designs are also investigated. Under the assumption of effect sparsity, a design with good projections onto small subsets of factors can provide useful information after the small number of active factors have been identified.
Experimental design is used extensively in a wide range of scientific and industrial investigations. 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 can be observed, and how to choose a good fraction is an important issue. In recent years, such fractional factorial designs have received considerable attention, mainly due to the success in applying them to conduct experiments for improving quality and productivity in industrial manufacturing. This research is to study the construction of efficient designs to extract more information. Experimenters will be benefited by having a rich source of new and good designs, and will be able to run their experiments more efficiently. Better industrial experiments can improve the quality of products and reduce production cost.
