A Textile Study
/****************************************************************/
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: ADXEG7 */
/* TITLE: A Textile Study */
/* PRODUCT: QC */
/* SYSTEM: ALL */
/* KEYS: Design of Experiments,Factorial Designs */
/* PROCS: */
/* DATA: */
/* REF: Box, G.E.P., and Cox, D.R. "An Analysis of */
/* Transformations". Journal of the Royal */
/* Statistical Society, B-26, pp. 211-243. */
/* MISC: ADX Macros are stored in the AUTOCALL library */
/* */
/* A simple 3**3 design was used to study the effects different */
/* factors on the failure of a yarn manufacturing process. The */
/* design factors are */
/* * the length of test specimins of yarn, ranging from 250 */
/* to 350 mm, */
/* * the amplitude of the loading cycle, ranging from 8 to */
/* 10 mm, */
/* * the load, ranging from 40 to 50 grams. */
/* The measured response was time (in cycles) until failure, */
/* but it could as easily have been the inverse of this */
/* quantity, the failure rate. An analysis using %adxtrans */
/* reveals a clear optimum power transformation right around */
/* the log transform. */
/* */
/****************************************************************/
/*--------------------------------------------------------------*/
/* EXAMPLE 7: A TEXTILE STUDY */
/* SOURCE: BOX AND COX (1964). */
/*--------------------------------------------------------------*/
/*
/ For this example, we need only general macros, since we will
/ use FACTEX itself to create the design: if we haven't already
/ included them, we do so now.
/---------------------------------------------------------------*/
%adxgen;
%adxinit /* Initialize ADX environment. */
/*
/ The design itself is a simple 3**3 factorial: we use FACTEX
/ directly.
/---------------------------------------------------------------*/
proc factex;
factors len amp load / nlev=3;
output out=yarn len nvals=(250 300 350)
amp nvals=( 8 9 10)
load nvals=( 40 45 50);
run;
/*
/ Normally, we would want to write a report which will print
/ the runs in the design in a randomized order and provide space
/ for a researcher to fill in the values of the response: use the
/ following to do this:
/ %adxrprt(yarn,failcyc)
/ Assuming this has been done, we add the data to the design
/ with the following DATA step.
/---------------------------------------------------------------*/
data yarn; set yarn;
input failcyc @@;
output;
cards;
674 370 292 338 266 210 170 118 90
1414 1198 634 1022 620 438 442 332 220
3636 3184 2000 1568 1070 566 1140 884 360
;
/*
/ We need to recode this data so that we can analyze it.
/---------------------------------------------------------------*/
%adxcode(yarn,yarn,len amp load)
/*
/ Create the cross-product and squared terms of the second order
/ model.
/---------------------------------------------------------------*/
%adxqmod(yarn,yarn,len amp load,1)
/*
/ And do the transformation analysis, relying on the default
/ model set up by %adxqmod.
/---------------------------------------------------------------*/
%adxtrans(yarn,tranyarn,failcyc)
/*--------------------------------------------------------------*/
/* */
/* The estimated power transformation is lambda = -0.2, but the */
/* 95 % confidence interval contains lambda = 0, which */
/* corresponds to the log transform. The analysis indicates */
/* that the transformation really *is* required: not only does */
/* the residual mean square dip sharply in the neighborhood of */
/* the optimum, but whereas almost *all 10* of the parameters */
/* of the model are significant when the original responses are */
/* analyzed, only the four of them are with respect to the */
/* transformed data, the intercept and the three linear effects */
/* of the factors. In this case, working with the data in the */
/* original metric clouds the issue and impedes scientific */
/* understanding of the underlying process. */
/* */
/*--------------------------------------------------------------*/
/*
/ If you have SAS/GRAPH licensed, try the following code to
/ produce a high-resolution plot of the T-values for the
/ parameters versus lambda.
/ symbol1 i=spline; symbol2 i=spline; symbol3 i=spline;
/ symbol4 i=spline; symbol5 i=spline; symbol6 i=spline;
/ symbol7 i=spline; symbol8 i=spline; symbol9 i=spline;
/ symbol10 i=spline;
/ proc gplot data=adxreg;
/ plot (intercept &adxfit)*adxlam / overlay;
/ run;
/---------------------------------------------------------------*/