Construction of fractional factorial split-plot designs with weak minimum aberration

Fractional factorial split-plot (FFSP) designs with minimum aberration have received much attention in industrial experiments. But they are not so easy to be constructed for the cases when there are many whole plot (or sub-plot) factors and only few sub-plot (or whole plot) factors. Weak minimum aberration is a weak version of minimum aberration. Based on the theory of complementary designs, this paper provides some theoretical results which are useful for constructing FFSP designs with weak minimum aberration for these cases. From these results, many such FFSP designs are constructed and tabulated, and it is further shown that quite a few of them are also minimum aberration designs