Nonregular Designs: Classification, Optimality and Construction

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Proposal ID: DMS-0204009PI: Hongquan XuTitle: Nonregular designs: Classification, optimality and constructionNonregular designs, such as Plackett-Burman designs and many other orthogonal arrays, are widely used in practice due to their run size economy and flexibility. However, many commonly used nonregular designs are not optimal. Unlike regular designs, which have been studied thoroughly in recent years, theory and construction of nonregular designs are still very primitive and urgently needed. The objectives of this proposed research are to classify and construct optimal nonregular designs. In the classification part, general frameworks and novel approaches are proposed for investigating the following important issues: estimation capacity, design efficiency, projection properties, and aliasing structure. In the construction part, novel methods and algorithms are proposed for constructing optimal nonregular designs for a wide variety of situations, including supersaturated designs and block designs. Coding theory will be employed to develop general results for multi-level and mixed-level nonregular designs.Experimental design is an effective and commonly used tool in scientific investigation. Over the last century, it has made tremendous impact in many areas of research, including agriculture, biology, manufacturing and high-tech industries, and will continue to do so for the foreseeable future. While most of the existing research has concentrated on the study of regular designs, this proposed research focuses on the study of nonregular designs. Nonregular designs are widely used in practice due to their run size economy and flexibility, for example, Taguchi designs for process improvement and quality control. However, it is important to note that many commonly used nonregular designs are not optimal. Unlike regular designs, which have been studied thoroughly in recent years, theory and construction of nonregular designs are still very primitive and urgently needed. The objectives of this proposed research are to classify and construct optimal nonregular designs. This proposal emphasizes an important interdisciplinary connection between error-correcting codes and factorial designs. The proposed work will develop fundamental results for nonregular designs, and will lead to remarkable new advances in design theory and better practice in experimentation.