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Optimal selection and ordering of columns in supersaturated designs |
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| Authors: | N NikiM Iwata H Hashiguchi S Yamada |
| Institution: | a Tokyo University of Science, Department of Management Science, Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan b DENSO Corporation, Showa-cho, Kariya, Aichi 448-8661, Japan c Saitama University, Graduate School of Science and Engineering, Shimo-Okubo, Sakura, Saitama 338-8570, Japan d University of Tsukuba, Graduate School of Business Sciences, Otsuka, Bunkyo-ku, Tokyo 112-0012, Japan |
| Abstract: | Two methods to select columns for assigning factors to work on supersaturated designs are proposed. The focus of interest is the degree of non-orthogonality between the selected columns. One method is the exhaustive enumeration of selections of p columns from all k columns to find the exact optimality, while the other is intended to find an approximate solution by applying techniques used in the corresponding analysis, aiming for ease of use as well as a reduction in the large computing time required for large k with the first method. Numerical illustrations for several typical design matrices reveal that the resulting “approximately” optimal assignments of factors to their columns are exactly optimal for any p. Ordering the columns in E(s2)-optimal designs results in promising new findings including a large number of E(s2)-optimal designs. |
| Keywords: | Corresponding analysis Exhaustive enumeration Factor assignment Non-orthogonality Optimal design |
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