Asymmetrical split-plot designs with clear effects

The fractional factorial split-plot (FFSP) design is an important experimental design both in theory and in practice. There is extensive literature on the two-level FFSP design and its various variants. However, there is little work on the s-level FFSP design and its variants in the asymmetrical (i.e., mixed-level) case, where s is any prime or prime power. Such designs are commonly used e.g. in agriculture, medicine and chemistry. This paper provides the necessary and sufficient conditions for the existence of resolution III or IV regular s(n1+n2)-(k1+k2)(sr) designs which contain clear main effects or two-factor interaction components. In particular, the sufficient conditions are proved through constructing the corresponding designs, and some examples are provided to illustrate the construction methods.