Construction of response surface designs for qualitative and quantitative factors

A general approach is proposed for constructing response surface designs of economical size for qualitative and quantitative factors. It starts with an efficient design (e.g. central composite design) for the quantitative factors and then partitions the design points into groups corresponding to different level combinations of the qualitative factors. Good designs are selected to ensure high estimation efficiency for models that reflect some stated objectives. The method is illustrated with the construction of designs for one qualitative factor. Some designs for two qualitative factors are constructed and extensions considered. Algorithmic construction of designs is briefly discussed.