Some theoretical results for fractional factorial split-plot designs

Fractional factorial (FF) designs are commonly used in industrial experiments to identify factors affecting a process. When it is expensive or difficult to change the levels of some of the factors, fractional factorial split-plot (FFSP) designs represent a practical design option. Though FFSP design matrices correspond to FF design matrices, the randomization structure of the FFSP design is different. In this paper we discuss the impact of randomization restrictions on the choice of FFSP designs and develop theoretical results. Some of these results are very closely related to those available for FF designs while others are more specific to FFSP designs and are more useful in practice. We pay particular attention to the minimum aberration criterion (MA) and emphasize the differences between FFSP and FF designs.