R-optimal designs for mixture experiments

A new class of optimality criteria i.e. R-optimality criterion is suggested, which depends on a joint confidence rectangle for the parameter estimation. And its equivalence theorem and invariance property which allows an easy calculation of optimal designs on many linearly transformed design spaces are given. For the full quadratic model widely used in the analysis of the experiments involving mixture is choosed as an example for the R-optimal designs. It is proved that in the R-optimal designs vertices and barycentres of depth 1 on the simplex Sq-1 are support points.