Efficient construction of split-plot design catalogs using graphs

Fractional-factorial split-plot designs are useful variants of the traditional fractional-factorial designs. They incorporate practical constraints on the randomization of experiment runs. Catalogs of split-plot designs are useful to practitioners as they provide a means of selecting the best design suitable for their task. However, the construction of these catalogs is computationally challenging as it requires comparing designs for isomorphism, usually in a large collection. This article presents an efficient approach for constructing these catalogs by transforming the design isomorphism problem to a graph isomorphism problem. A new graph representation of split-plot designs is presented to achieve this aim. Using examples it is shown how these graph representations can be extended to certain other classes of factorial designs for solving the (corresponding) design isomorphism problem. The efficacy of this approach is demonstrated by presenting catalogs of two-level regular fractional factorial split-plot designs of up to 4096 runs, which is much larger than available in existing literature.