Abstract: Considering general prime or prime powered factorials, we give a finite projective geometric formulation for regular fractional factorial split-plot designs. This provides a unified framework for such designs and facilitates their systematic study under the criteria of minimum aberration and minimum secondary aberration; the latter criterion is considered to achieve finer discrimination. We investigate the role of complementary subsets in this context and observe that, unlike in classical fractional factorials, two such complementary subsets have to be handled simultaneously. Criteria based on estimation capacity are also studied to provide further statistical justification for our results. Finally, applications of the results to specific cases are summarized as tables.
Key words and phrases: Complementary subsets, finite projective geometry, minimum secondary aberration, two-phase randomization, sub plot, whole plot, word-length pattern.