An isomorphism check for two-level fractional factorial designs
- 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 method=retrieve&_udi=B6V0M-4NTJH0W-1&_mathId=mml33&_user=10&_cdi=5650&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=f33b9506f46903202c889c5f8107b2eb" title="Click to view the MathML source">
4 to situations with 12, 13, 14, 15 and 16 factors, 256- and 512-run designs with resolution method=retrieve&_udi=B6V0M-4NTJH0W-1&_mathId=mml34&_user=10&_cdi=5650&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=7bccdb7b7aea5422a03ffb81106ab9d2" title="Click to view the MathML source">5 and method=retrieve&_udi=B6V0M-4NTJH0W-1&_mathId=mml35&_user=10&_cdi=5650&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=9c1b8178d6216c90ec6d6f5b4c9dd8ed" title="Click to view the MathML source">
17 factors and 1024-run even designs with resolution method=retrieve&_udi=B6V0M-4NTJH0W-1&_mathId=mml36&_user=10&_cdi=5650&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=47c701fc63bf81c154d32314bccfdd62" title="Click to view the MathML source">6 and method=retrieve&_udi=B6V0M-4NTJH0W-1&_mathId=mml37&_user=10&_cdi=5650&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=af2e9aea58377f52c642804f96503a3c" title="Click to view the MathML source">18 factors.
4 to situations with 12, 13, 14, 15 and 16 factors, 256- and 512-run designs with resolution method=retrieve&_udi=B6V0M-4NTJH0W-1&_mathId=mml34&_user=10&_cdi=5650&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=7bccdb7b7aea5422a03ffb81106ab9d2" title="Click to view the MathML source">5 and method=retrieve&_udi=B6V0M-4NTJH0W-1&_mathId=mml35&_user=10&_cdi=5650&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=9c1b8178d6216c90ec6d6f5b4c9dd8ed" title="Click to view the MathML source">17 factors and 1024-run even designs with resolution method=retrieve&_udi=B6V0M-4NTJH0W-1&_mathId=mml36&_user=10&_cdi=5650&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=47c701fc63bf81c154d32314bccfdd62" title="Click to view the MathML source">6 and method=retrieve&_udi=B6V0M-4NTJH0W-1&_mathId=mml37&_user=10&_cdi=5650&_rdoc=22&_acct=C000050221&_version=1&_userid=10&md5=af2e9aea58377f52c642804f96503a3c" title="Click to view the MathML source">18 factors.