Some Results on Fractional Factorial Split-Plot Designs with Multi-Level Factors

Fractional factorial split-plot (FFSP) designs have received much attention in recent years. In this article, the matrix representation for FFSP designs with multi-level factors is first developed, which is an extension of the one proposed by Bingham and Sitter (1999b Bingham , D. , Sitter , R. R. ( 1999b ). Some theoretical results for fractional factorial split-plot designs . Ann. Statist. 27 : 1240 – 1255 . [Google Scholar]) for the two-level case. Based on this representation, periodicity results of maximum resolution and minimum aberration for such designs are derived. Differences between FFSP designs with multi-level factors and those with two-level factors are highlighted.