Design and Analysis of Experiments for Screening, Optimization and Robustness

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Abstract:The goal of this proposal is to study three important aspects of experimentation: screening, optimization and robustness. Section I proposes a novel approach to factor screening and response surface exploration by using a single design and experiment to achieve both objectives. This differs from the standard response surface methodology, which employs separate designs for factor screening and for response surface exploration. New concepts, theory and analysis are proposed, which include a two-stage analysis and a projection-efficiency criterion. Four problems are to be studied: (i) a theory for eligible projections in regular designs, (ii) combinatorial and algorithmic construction of optimal nonregular designs, (iii) connection with the maximum estimation capacity criterion, (iv) sensitivity of response surface exploration to errors in factor screening and a Bayesian alternative to the two-stage analysis. Section II addresses a fundamental and practically important issue of optimal assignment of factors to columns of a design matrix. Existing work can only be applied to regular fractional factorial designs and nonregular designs with two-level factors. By defining a B-contamination criterion and employing the Kronecker calculus, we propose an approach that can handle very general designs. Three problems are to be studied: (i) Finding expressions for the contamination terms, (ii) characterization in terms of complementary designs, (iii) extensions to blocked designs. Section III addresses the issue of optimal selection of experimental plans for robust parameter design. When the experimental cost is proportional to the total run size, the cross array format can be quite costly and the single array format becomes an attractive option. An important question is how to select single arrays optimally and according to what criteria? By using an effect ordering principle, we propose to define new criteria and use them to select optimal single arrays. Statistical design and analysis of experiments is an effective and commonly used tool in scientific and engineering investigation. It has made significant impact in many areas of research and development such as manufacturing, electronics, materials, agriculture and energy. It will continue to make important contributions by innovation in methodological and theoretical development and applications in new areas such as biotechnology, drug discovery, and information technology. Potential gains from using the proposed new methods include savings in experimental runs, experimentation time, and discovery of new/better engineering designs and products. The results on factor assignment will provide clear guidelines on the assignment of factors and a substantial improvement over the prevailing practice of making arbitrary and often suboptimal assignment. Parameter design has become a major tool for variation reduction and product and process improvement. The proposed work will develop new and more economical and efficient techniques for conducting such experiments.