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Yarn Elongation: A Mixture Experiment

 /****************************************************************/
 /*              S A S   S A M P L E   L I B R A R Y             */
 /*                                                              */
 /*    NAME: ADXEG5                                              */
 /*   TITLE: Yarn Elongation: A 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, pp. 32-35.             */
 /*    MISC: ADX Macros are stored in the AUTOCALL library       */
 /*                                                              */
 /*                                                              */
 /* Cornell (1981) describes the use of a simplex-lattice design */
 /* to study the properties of different yarn blends for         */
 /* draperies. The three constituents are                        */
 /*      * polyethylene  (PETHYLN),                              */
 /*      * polystyrene   (PSTYREN), and                          */
 /*      * polypropylene (PPROPYL).                              */
 /* Only pure blends and binary blends are to be studied, so a   */
 /* simplex-lattice design of order 2 is called for.  The yarn   */
 /* characteristic to be studied is                              */
 /*      * thread elongation (ELONG)                             */
 /*                                                              */
 /****************************************************************/




 /*--------------------------------------------------------------*/
 /*  EXAMPLE 5:  A SIMPLEX-LATTICE DESIGN FOR STUDYING YARN.     */
 /*                      SOURCE:  CORNELL (1981).                */
 /*--------------------------------------------------------------*/

 /*
 /  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.  */

 /*
 /  The design is quite easy to construct.
 /---------------------------------------------------------------*/
 %adxsld(yarn,pethyln pstyren ppropyl,2)

 /*
 /  We can add the elongation data to the design with a DATA step:
 /  two runs were made in the actual experiment for each pure
 /  blend, and three for each 50:50 blend.
 /---------------------------------------------------------------*/
 data yarn; set yarn; drop npos i;
    array x{3} pethyln pstyren ppropyl;

    npos = 0;
    do i = 1 to 3;
       npos = npos + (x{i} > 0);
       end;

    if (npos = 1) then do i = 1 to 2;
       input elong @@;
       output;
       end;
    else do i = 1 to 3;
       input elong @@;
       output;
       end;
    cards;
 16.8 16 10 9.7 11.8 8.8 10 17.7 16.4 16.6 15 14.8 16.1 11 12.4
 run;

 /*
 /  Fit a general quadratic model to the data, except for the
 /  intercept term (because of the sum-to-1 constraint for the
 /  mixture levels.)
 /---------------------------------------------------------------*/
proc glm;
   model elong = pethyln|pstyren|ppropyl@2 / noint;
run;