Macros for the Design and Analysis of Experiments

Mixture Design Macros: ADXMIX File

The ADXMIX file contains five macros for use in mixture experiments. In a mixture experiment, the independent factors are proportions of different components of a blend. For example, if you want to optimize the tensile strength of stainless steel, then factors of interest might be the proportions of iron, copper, nickel, and chromium in the alloy. The fact that the proportions of the different factors must sum to 100% complicates the design as well as the analysis of mixture experiments.

When the mixture components are subject only to the constraint that they must sum to one, there are standard designs for fitting standard models. When mixture components are subject to additional constraints, such as a maximum and minimum value for each component, nonstandard designs are called for. The ADXMIX file contains macros for both the unconstrained and constrained situations as follows:

ADXFILL adds interior points to any design with a convex feasible region.

ADXMAMD constructs McLean-Anderson mixture designs. McLean and Anderson (1966) suggest using the vertices of the feasible region when fitting first- or second-order models.

ADXSCD constructs simplex-centroid designs. These are standard designs.

ADXSLD constructs simplex-lattice designs. These are standard designs.

ADXXVERT constructs extreme vertices designs. Snee and Marquardt (1974) and Snee (1975) suggest generating vertices and centroids of the faces of the constrained region, then choosing the design points from this set. ADXXVERT constructs the set of vertices and face-centroid points. If the set is too large to run as a design, you can use the OPTEX procedure to choose an optimal subset.

The next five sections give details on these macros.

Mixture Design Macros: ADXMIX File

ADXFILL: Filling in the Design Region

ADXMAMD: Construct McLean-Anderson Mixture Designs

ADXSCD: Construct Simplex-Centroid Designs

ADXSLD: Construct Simplex-Lattice Designs

ADXXVERT: the XVERT Algorithm

ADXFILL	adds interior points to any design with a convex feasible region.
ADXMAMD	constructs McLean-Anderson mixture designs. McLean and Anderson (1966) suggest using the vertices of the feasible region when fitting first- or second-order models.
ADXSCD	constructs simplex-centroid designs. These are standard designs.
ADXSLD	constructs simplex-lattice designs. These are standard designs.
ADXXVERT	constructs extreme vertices designs. Snee and Marquardt (1974) and Snee (1975) suggest generating vertices and centroids of the faces of the constrained region, then choosing the design points from this set. ADXXVERT constructs the set of vertices and face-centroid points. If the set is too large to run as a design, you can use the OPTEX procedure to choose an optimal subset.