Mixture experiments entail changing the component proportions of the independent variables and examining the changes in the response data. Mixture experiments have the factor components adding up to a certain value, hence the components cannot be varied independently. Due to this distinction on design space for mixture experiments, models such as the ones used for factorial experiments cannot be fit. When the factor components are subjected to the condition that they must add up to 1(100%), they form simplex-shaped regions which are fitted using standard mixture design models. However, there arise situations when mixture components are subjected to additional lower and/or upper constraints on component proportions notwithstanding the fact that the components must sum up to 1(100%) forming irregular-shaped regions. This paper discusses optimal design as an approach and method for designing and analyzing mixture experiments arising from such irregular-shaped design spaces. To illustrate the techniques used and their application in agricultural research, a hypothetical example of a 3-component constrained mixture design is employed. Using the point-and-click ADX interface of SAS, given the objective of the experiment, the mixture components and the constraints are selected in order to identify the experimental region. The response variable is identified and an appropriate model is selected. An experimental design is selected that is sufficient to fit the proposed model and experimental data is supplied to determine the feasible design space. The data is then analyzed to determine the influence of each factor on the response of interest and graphical techniques employed for interpreting component effects. Design efficiencies are evaluated with respect to the D-, A- and G-optimality criterions. We establish that the optimal designs can be developed empirically to increase the productivity and improve quality in agricultural research.

constrained mixture experiments, optimal design, optimality criteria, D-efficiency, A-efficiency, G-efficiency, ADX interface.