Optimal orthogonal block designs for a quadratic mixture model for three components

In experiments with mixtures that involve process variables, if the response function is expressed as the sum of a function of mixture components and a function of process variables, then the parameters in the mixture part and in the process part can be estimated independently using orthogonal block designs. This paper is concerned with such a block design for parameter estimation in the mixture part of a quadratic mixture model for three mixture components. The behaviour of the eigenvalues of the moment matrix of the design is investigated in detail, the design is optimized according to E- and A-optimality criteria, and the results are compared together with a Known result on D-optimality. It is found that this block design is robust with respect to these different optimality criteria against the shifting of experimental points. As a result, we recommend experimental points of the form (a, b, c) in the simplex S-2, where c = 0, b = 1-a, and a can be any value in the range 0.17+/- 0.02.