Abstract: In this paper, we propose some new necessary and sufficient conditions for identifying isomorphism in two-level fractional factorial designs, using a parallel flats structure. A new algorithm for checking isomorphism is provided accordingly. The proposed algorithm is simple and general, and can be used for either regular or nonregular designs. By taking advantage of the parallel flats structure when it exists, the method is much faster than current methods for assessing the isomorphism of nonregular two-level designs. Examples are given to illustrate the results. An efficient implementation of the proposed algorithm in Matlab can be found in the online Supplementary Material.

Key words and phrases: Algorithm, equivalent group, parallel flats, two-level fractional factorial.