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Details of the OPTEX Procedure 
See OPTEX11 in the SAS/QC Sample Library 
Suppose you want a 15run experiment for three mixture factors X1, X2, and X3; furthermore, suppose that X3 cannot account for any more than 75% of the mixture. You can use the ADXXVERT macro (see "ADXXVERT: the XVERT Algorithm" ) to construct a list of candidate points for the design and then use the OPTEX procedure to select the design runs optimally for a given model. However, informationbased criteria such as D and Aefficiency tend to push the design to the edges of the candidate space, leaving large portions of the interior relatively uncovered. For this reason, it is often a good idea to augment a Doptimal design with some points chosen according to Uoptimality, which seeks to cover the candidate region as well as possible.
The collection of macros for experimental designs described
at Appendix E,"Macros for the Design and Analysis of Experiments"
includes several macro programs for working with
mixture designs. For example, the following statements invoke the
ADXXVERT macro to construct and plot the candidate set:
%adxgen %adxmix %adxxvert(a,x1 / x2 / x3 0  .75); data a; set a; w1 = (x1 + x2); w2 = (x1  x2); proc plot data=a; plot w1*w2; run;
The result, shown in Output 24.10.1, is a "quickanddirty" plot of the vertices, the edge centroids, and the overall centroid for the feasible region. The constraint effectively "cuts off" the top of the usual simplex.
Output 24.10.1: Vertices and Centroids for Constrained Mixture DesignYou can use the OPTEX procedure to select 10 optimal points for estimating a secondorder model in the mixture factors.
proc optex data=a seed=60868 nocode; model x1x2x3@@2 / noint; generate n=10; output out=b; data b; set b; w1 = (x1 + x2); w2 = (x1  x2); proc plot data=b; plot w1*w2; run;As shown in Output 24.10.2, the Doptimal design omits some of the candidate points and replicates others. Output 24.10.2: Doptimal Constrained Mixture Design

%adxfill(a,x1 x2 x3); data a; set a; w1 = (x1 + x2); w2 = (x1  x2); proc plot data=a; plot w1*w2; run;The ADXFILL macro simply computes all pairwise averages of points in A and appends them to A; see "ADXFILL: Filling in the Design Region" for more details. The results are shown in Output 24.10.3. Output 24.10.3: Filled Candidate Region for Constrained Mixture Design

proc optex data=a seed=4321 nocode; model x1 x2 x3 / noint; generate n=15 augment=b criterion=u; output out=c; data c; set c; w1 = (x1 + x2); w2 = (x1  x2); proc plot data=c; plot w1*w2; run;Output 24.10.4 shows that the Uoptimal design fills in the candidate region in much the same way that you might construct the design by visually assigning points. That is, the general approach using the OPTEX procedure agrees with visual intuition for this small problem. Moreover, the general approach yields an appropriate design for higher dimensional problems that cannot be visualized. Output 24.10.4: Doptimal Constrained Mixture Design Filled In Uoptimally

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