Mixture designs

Mixture designs allow to optimize formulations of a product. Design them in Excel using the XLSTAT add-on statistical software.

What are mixture designs

Mixture designs are used to model the results of experiments where these relate to the optimization of formulations. The resulting model is called mixture distribution.

When the concentrations of the n components are not submitted to any constraint, the experimental design is a simplex, that is to say, a regular polyhedron with n vertices in a space of dimension n-1. For example, for a mixture of three components, the experimental field is an equilateral triangle; for 4 constituents it is a regular tetrahedron.

Creating mixture designs therefore consist of positioning regularly the experiences in the simplex to optimize the accuracy of the model. The most conventional designs are Scheffé’s designs, Scheffé-centroid designs, and augmented designs.

If constraints on the components of the model are introduced by defining a minimum amount or a maximum amount not to exceed, then, the experimental domain can be a simplex, an inverted simplex (also called simplex B) or a any convex polyhedron. In the latter case, the simplex designs are no longer usable.

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