Optimal designs for mixture models with amount constraints

Optimal designs for mixture experiments defined on the regular simplex are widely available but a lot fewer optimal designs are available for mixture experiments defined on the q-dimensional design space: S∗q={(z1,…,zq)′∈Rq|z1+⋯+zq≤1,zi≥0,i=1,…,q}. This paper proposes a flexible class of models for mixture experiments defined on S∗q and gives a simple method for finding DD and AA-optimal designs for the models using optimal designs available for the mixture experiments defined on the regular simplex.