Design of experiments with both mixture and qualitative factors

while the remaining L factors are qualitative, i.e. they take only a distinct number of possible values. The conditions for optimality of approximate designs for the general case of experiments with qualitative and quantitative factors have been established by Kurotschka (1981, 1987) and Wierich (1986). Exact designs for such experiments are described in Atkinson and Donev (1989), but neither set of researchers gives any special treatment to experiments with mixtures. The mixture constraint (1), however, introduces some special features which it is the purpose of this paper to investigate. In Section 2 some useful properties of the mixture experiments are listed. In Section 3 models and optimality conditions for experiments with mixture and qualitative factors are established. Discussion with examples is given in Section 4. In Section 5 more general mixture experiments are considered, in which the response depends on the amount of the mixture as well as on the proportions of its components. Experiments of this kind are common in such areas as chemistry, medicine and agriculture.