An isomorphism check for two-level fractional factorial designs.

*(English)*Zbl 1130.62078Summary: 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 D. Bingham and R. R. Sitter [Minimum aberration fractional factorial split-plot designs. Technometrics 41, 62–70 (1999)] search algorithm and the isomorphism check algorithm of J. B. Clark and A. M. Dean [Equivalence of fractional factorial designs. Stat. Sin. 11, No. 2, 537–547 (2001; Zbl 0980.62058)] 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 \(\geqslant 4\) to situations with 12, 13, 14, 15 and 16 factors, 256- and 512-run designs with resolution \(\geqslant 5\) and \(\leqslant 17\) factors and 1024-run even designs with resolution \(\geqslant 6\) and \(\leqslant 18\) factors.

##### MSC:

62K15 | Factorial statistical designs |

65C60 | Computational problems in statistics (MSC2010) |

62Q05 | Statistical tables |

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\textit{C. D. Lin} and \textit{R. R. Sitter}, J. Stat. Plann. Inference 138, No. 4, 1085--1101 (2008; Zbl 1130.62078)

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##### References:

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