Mixture Experiments in the Interior: Yantram Designs

We introduce a very rich class of mixture designs in the interior of the simplex, which are useful when all experiments must constitute a complete mixture, that is, when none of the components is absent from the mixture. These designs are called yantram designs, as they are directly derivable from the Hindu yantrams, which are certain numerical configurations of positive integers having certain properties. Not only do these designs work well within the interior of the simplex, they can also be easily refined to satisfy the constraints, if there are any, on the mixture components. Leverage values for such designs are more evenly distributed among interior points compared to simplex-lattice or simplex-centroid designs, which tend to place higher leverages on the vertices or edge design points where the experiments may not be feasible.