Obtaining Non-isomorphic Two-level Regular Fractional Factorial Designs
Two fractional factorial designs are isomorphic if one can be obtained from the other by reordering the treatment combinations, relabeling the factor levels and relabeling 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) search algorithm, the isomorphism check algorithm of Clark and Dean (2001) with our proposed isomorphism check. The algorithm is used to extend the known set of existing non-isomorphic 128-run designs to situations with 12, 13, 14, and 15 factors.
This type of interdisciplinary work is a hallmark of our program in Applied Statistics at Simon Fraser University. For more information, please contact Chunfang Lin (clinistat.sfu.ca) or her supervisor Randy Sitter (sitterstat.sfu.ca).