Design of Experiments Guide • Mixture Designs
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Mixture Designs
 
The mixture designer supports experiments with factors that are ingredients in a mixture. You can choose among several classical mixture design approaches, such as simplex, extreme vertices, and lattice. For the extreme vertices approach you can supply a set of linear inequality constraints limiting the geometry of the mixture factor space.
The properties of a mixture are almost always a function of the relative proportions of the ingredients rather than their absolute amounts. In experiments with mixtures, a factor's value is its proportion in the mixture, which falls between zero and one. The sum of the proportions in any mixture recipe is one (100%).
Designs for mixture experiments are fundamentally different from those for screening. Screening experiments are orthogonal. That is, over the course of an experiment, the setting of one factor varies independently of any other factor. Thus, the interpretation of screening experiments is relatively simple, because the effects of the factors on the response are separable.
With mixtures, it is impossible to vary one factor independently of all the others. When you change the proportion of one ingredient, the proportion of one or more other ingredients must also change to compensate. This simple fact has a profound effect on every aspect of experimentation with mixtures: the factor space, the design properties, and the interpretation of the results.
Because the proportions sum to one, mixture designs have an interesting geometry. The feasible region for the response in a mixture design takes the form of a simplex. For example, consider three factors in a 3-D graph. The plane where the sum of the three factors sum to one is a triangle-shaped slice. You can rotate the plane to see the triangle face-on and see the points in the form of a ternary plot.
Mixture Design
Contents 
Mixture Design Types
The Optimal Mixture Design
The Simplex Centroid Design
Creating the Design
Simplex Centroid Design Examples
The Simplex Lattice Design
The Extreme Vertices Design
Creating the Design
An Extreme Vertices Example with Range Constraints
An Extreme Vertices Example with Linear Constraints
Extreme Vertices Method: How It Works
The ABCD Design
The Space Filling Design
FFF Optimality Criterion
Set Average Cluster Size
Linear Constraints
A Space Filling Example
A Space Filling Example with a Linear Constraint
Creating Ternary Plots
Fitting Mixture Designs
Whole Model Tests and Analysis of Variance Reports
Understanding Response Surface Reports
A Chemical Mixture Example
Create the Design
Analyze the Mixture Model
The Prediction Profiler
The Mixture Profiler
A Ternary Plot of the Mixture Response Surface