New non-isomorphic detection methods for orthogonal designs

Two fractional factorial designs are called isomorphic if one can be obtained from the other by relabeling the factors, reordering the runs and switching the levels of factors. Given a set of all orthogonal designs (ODs) with n runs, q levels and s factors, it may have several non-isomorphic subclasses. Once a new OD with this design size is generated, it is interesting to know which subclass it belongs to. In this paper, we review several existing methods, which can classify newly generated ODs to the correct non-isomorphic subclass. We also propose two new non-isomorphic detection methods. They can be utilized for the design classification purpose and take some advantages over the existing methods in terms of computation efficiency and classification capability.