A Constrained Mixture Experiment
/****************************************************************/
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: ADXEG6 */
/* TITLE: A Constrained Mixture Experiment */
/* PRODUCT: QC */
/* SYSTEM: ALL */
/* KEYS: Design of Experiments, */
/* PROCS: */
/* DATA: */
/* REF: Cornell, J.A. (1981). Experiments with Mixtures. */
/* New York: John Wiley & Sons. */
/* Snee, R.D. (1975). "Experimental Designs for */
/* Quadratic Models in Constrained Mixture Spaces." */
/* Technometrics, 17:2, pp. 149-159. */
/* MISC: ADX Macros are stored in the AUTOCALL library */
/* */
/* */
/* Snee (1975) discusses a lubricant blending study in which */
/* there are four factors in the blend. Here are the components */
/* and the respective ranges of their contribution to the blend:*/
/* Additive : 7% to 18% */
/* Component A: 0% to 30% */
/* Component B: 37% to 70% */
/* Component C: 0% to 15% */
/* */
/****************************************************************/
/*--------------------------------------------------------------*/
/* EXAMPLE 6: AN XVERT DESIGN FOR STUDYING LUBRICANT BLENDS. */
/* SOURCE: SNEE (1975). */
/*--------------------------------------------------------------*/
/*
/ For this example, we need only the mixture design macros: if we
/ haven't already included them, we do so now.
/---------------------------------------------------------------*/
%adxgen;
%adxmix;
%adxinit /* Initialize ADX environment. */
/*
/ Call %adxvert() with the appropriate constraints on the mixture
/ components. We can leave off the lower bounds of 0 for
/ components A and C, since this will be the default.
/---------------------------------------------------------------*/
%adxxvert(lube,Add .07-.18 /CompA -.3 /CompB .37-.7 /CompC -.15)
/*
/ The actual design which Snee used was composed of a subset of
/ the 33 mixture component combinations found by XVERT: centroids
/ were chosen to be included in the design on the basis of the
/ dimension of the face with which they were associated and the
/ average distance from the vertices of the face. The following
/ DATA step will choose
/ Snee's design from the set of combinations found by XVERT.
/---------------------------------------------------------------*/
data sneelube; set lube;
if ( (dimen = 0) /* All vertices */
| ((dimen = 1) & (dist > .2)) /* Make it harder for edge */
| ((dimen = 2) & (dist > .1)) /* centroids than faces */
| (dimen = 3) ); /* The overall centroid */
run;