What is a mixture design?

Mixture experiments are a special class of response surface experiments in which the product under investigation is made up of several components or ingredients. Designs for these experiments are useful because many product design and development activities in industrial situations involve formulations or mixtures. In these situations, the response is a function of the proportions of the different ingredients in the mixture. For example, you might be developing a pancake mixture that is made of flour, baking powder, milk, eggs, and oil. Or, you might be developing an insecticide that blends four chemical ingredients.

In the simplest mixture experiment, the response (the quality or performance of the product based on some criterion) depends on the relative proportions of the components (ingredients). The amount of components, measured in weights, volumes, or some other units, add up to a common total. In contrast, in a factorial design, the response varies depending on the amount of each factor.

Minitab provides three designs (simplex centroid, simplex lattice, and extreme vertices) and analyzes from three types of experiments:

Mixture: The response is assumed to only depend on the proportions of the components in the mixture. For example, paint color only depends on the pigments used.
Mixture-process variable: The response is assumed to depend on the relative proportions of the components and the process variables, which are factors in an experiment that are not part of the mixture, but might affect the blending properties of the mixture. For example, the flavor of a cake depends on the cooking time and cooking temperature, and the proportions of the cake ingredients.
Mixture-amount: The response is assumed to depend on the proportions of the components and the amount of the mixture. For example, the yield of a crop depends on the proportions of the insecticide ingredients and the amount of the insecticide applied.