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.
Statistical design of experiments is used extensively 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. When a large number of factors have to be studied but the experimental runs are expensive, it is not feasible to observe all possible combinations of the factors. This project was concerned with how to choose good small subsets of the factor combinations, called fractional factorial designs, for experimentation. In particular, the Principal Investigator studied the so-called multi-stratum experiments which have multiple sources of errors that arise from complicated structures of the experimental units. It was shown how recent work on multistratum fractional factorial designs can be set in a general and unifying framework. The research provided a better understanding of some of the important issues ranging from modeling and analysis to design construction. The Principal Investigator also proposed a general optimality criterion for design selection. The general theory was applied to find optimal and efficient designs for many different types of multistratum experiments. Practically useful templates for constructing multistratum fractional factorial designs were also developed. These templates facilitate systematic and simple construction of the design layouts and eliminate the need to check some conditions for design eligibility required by the traditional methods. During the grant period, the Principal Investigator wrote seven papers, six of which have appeared, and one has been accepted for publication. He also finished a 409-page book on the theory of factorial design. This book, to be published in December 2013, contains many results obtained with the supprot of this grant. Intellectual Merit: The research provided a unifying general theory. Such theoretical advances can help enhance the understanding of fundamental issues. Even for the practical problem of constructing efficient designs, the theory can either provide direct answers or guide the computation by substantially cutting down unnecessary searches to make the solution feasible. Broader impacts. Experimenters can 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, some of the results obtained can be appied to experiments with multiple processing stages, which often arise in industrial applications. Better industrial experiments can improve the quality of products and reduce production cost. Since the proposed research deals with some basic issues, the results developed can be included in a graduate course on experimental design.
