An isomorphism check for two-level fractional factorial designs

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• 作者：C. Devon Lin ; R.R. Sitter
• 关键词：Design equivalence ; Eigenvalue ; Eigenvector ; Hamming distance
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2008
• 期刊代码：36_03783758
• 类别：mt
• 出版时间：1 April 2008
• 卷：138
• 期：4
• 页码：1085-1101
• 文件大小：198 K

摘要

Two fractional factorial designs are isomorphic if one can be obtained from the other by reordering the treatment combinations, relabelling the factor levels and relabelling the factors. By defining a word-pattern matrix, we are able to create a new isomorphism check which is much faster than existing checks for certain situations. We combine this with a new, extremely fast, sufficient condition for non-isomorphism to avoid checking certain cases. We then create a faster search algorithm by combining the Bingham and Sitter [1999. Minimum aberration fractional factorial split-plot designs. Technometrics 41, 62–70] search algorithm, the isomorphism check algorithm of Clark and Dean [2001. Equivalence of fractional factorial designs. Statist. Sinica 11, 537–547] with our proposed isomorphism check. The algorithm is used to extend the known set of existing non-isomorphic 128-run two-level regular designs with resolution 4 to situations with 12, 13, 14, 15 and 16 factors, 256- and 512-run designs with resolution 5 and 17 factors and 1024-run even designs with resolution 6 and 18 factors.