ADXXVERT: the XVERT Algorithm

Macros for the Design and Analysis of Experiments

ADXXVERT: the XVERT Algorithm

%adxxvert(ds, vlst, m)

where

ds is the name of the SAS data set for the constructed design. This data set contains variables for design factors. Default names are used. The default names for design factors are T1, T2, T3, and so on.

vlst is a list of mixture components and their constraints. Separate information for different components with a slash (/) and specify each component as follows:
name loval-hival
where name gives the name of the component, loval gives the low value for the component, and hival gives the high value for the component. If you omit loval or hival, the defaults are 0 and 1, respectively.

m is the maximum order of centroid to be generated. By default, centroids of all orders are generated.

Use the ADXXVERT macro when your mixture factors are subject to constraints of the form

${low-value} & \leq & {component} & \leq & {high-value}$

In this situation, you cannot study a response over the entire mixture region, so you must use the ADXMAMD or ADXXVERT macros instead of the ADXSCD or ADXSLD macros. The ADXXVERT macro generates the points corresponding to the vertices of the feasible region and adds the centroids of the edges and generalized faces of the region as well, up to a specified order m. The resulting set of points can be too large for a design, but it provides a good candidate set from which to choose design points. Two additional variables are included in the data set, with the following values for each point:

DIMEN the dimension of the face of which the corresponding point is the centroid

DIST the average distance from the vertices on the face to the centroid

You can try to choose design points directly based in DIMEN and DIST, or you can use the OPTEX procedure to choose an optimal design from the set of candidate points; see Example 24.10 for a detailed example. For example, consider an experiment to study the effects of a lubricant additive on three-component lubricant blends. The additive and the three components are subject to restrictions as follows:

Mixture Component Range of Values

Additive (ADD) 7% to 18%

Component A (A) 0% to 30%

Component B (B) 37% to 70%

Component C (C) 0% to 15%

To construct the vertices and generalized face-centroids of the feasible region and output these points to the data set LUB, submit the following statements:

   %adxgen
   %adxmix
   %adxinit
   %adxxvert(lub,add .07 -.18 /a -.3 /b .37 -.7 /c -.15)

Since m is omitted in the ADXXVERT macro call above, centroids of all orders are generated and output to LUB.

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ds	is the name of the SAS data set for the constructed design. This data set contains variables for design factors. Default names are used. The default names for design factors are T1, T2, T3, and so on.
vlst	is a list of mixture components and their constraints. Separate information for different components with a slash (/) and specify each component as follows: name loval-hival where name gives the name of the component, loval gives the low value for the component, and hival gives the high value for the component. If you omit loval or hival, the defaults are 0 and 1, respectively.
m	is the maximum order of centroid to be generated. By default, centroids of all orders are generated.

DIMEN	the dimension of the face of which the corresponding point is the centroid
DIST	the average distance from the vertices on the face to the centroid

Mixture Component	Range of Values
Additive (ADD)	7% to 18%
Component A (A)	0% to 30%
Component B (B)	37% to 70%
Component C (C)	0% to 15%