Topics on Design of Experiments and Computer Experiments

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Experimental design is an effective and commonly used technique in investigations for applications in many areas of science, engineering and industry. The types of data structures dealt with are as varied as the applications. The objectives of the proposed research are to develop new design theories and methodology with certain data structures and provide efficient designs for practical use in both physical experiments and computer experiments. The proposal will address the critical issues on the design and analysis of physical and computer experiments with both qualitative and quantitative factors. It is expected that the proposed research will lead to new advances in design theory and better practice in experimentation. In conducting computer experiments, it has become common practice to select the design points that cover a design region as uniformly as possible. These so-called space-filling designs are used when little a priori information or background knowledge is available about which model would be appropriate, and inputs can be set to any value in the respective ranges. However, prior information or background knowledge might suggest some features of the response surfaces and thus certain models are more appropriate. Sequential design approaches will be introduced to generate designs that incorporate such information or knowledge. In many applications, factors are qualitative by nature. The problem of how to design and analyze computer experiment with both qualitative and quantitative factors are not yet completely solved. This proposal aims to develop new design methodology for such computer experiments. Fractional factorial designs are among the most widely used experimental plans in physical experiments. The proposed research will construct efficient fractional factorial designs for experiments with both qualitative and quantitative input factors and model-based designs. New classes of designs for factor screening and response surface exploration are introduced. Criteria for assessing such designs are proposed. The statistical properties and optimality of new designs are studied. Designs of variable resolution provide a good class of designs when certain two-factor interactions are negligible. This proposal systematically studies such designs from various aspects.