Optimal Experimental Designs and Response Surface Optimization

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Design of experiments is a popular tool in new product development and in process improvement and optimization. Optimal design provides interpretable and accurate inference at minimal costs. Methodology and computation issues are two main challenges in optimal design theory. The goal of the proposed research is to address various optimality problems in follow-up design, model-robust design, and response surface optimization. Fractional factorial designs are cost-efficient experimental plans for identifying and estimating important effects of multiple variables on a response. A fundamental problem for fractional factorial designs is that some effects are aliased and cannot be estimated. Follow-up design is one of the methods for resolving the problem. Alphabetical criteria are popular optimality criteria used to select optimal designs. The drawback of the criteria is that they depend on a pre-specified model. This is sometimes impossible since the true model is unknown in advance in practice. Thus the optimal designs obtained by these criteria may not be robust. Response surface optimization aims to select optimal operating settings to optimize the response. The challenge in this area is that it involves complicated statistical modelling and inference procedures. The application of such optimization includes manufacturing processes, such as assembly, machining, and welding, and service operations, such as banking systems and public transportation. The proposed research will develop new theory and methods to handle these issues in follow-up design, model-robust design, and response surface optimization. New optimality criteria will be proposed to construct optimal model-robust designs. My research program will involve extensive training of highly qualified personnel (HQP) in preparing them for future positions in both academia and industry. The proposed research will advance design theory and methodology and provide new economical experimental plans for experimenters in industrial, agricultural, pharmaceutical, manufacturing, engineering, and chemical sciences.