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Q Charts for Individual Measurements

 /****************************************************************/
 /*          S A S   S A M P L E   L I B R A R Y                 */
 /*                                                              */
 /*    NAME: SHWQCHT2                                            */
 /*   TITLE: Q Charts for Individual Measurements                */
 /* PRODUCT: QC                                                  */
 /*  SYSTEM: ALL                                                 */
 /*    KEYS: Shewhart Charts, Short Run Process Control, Q Chart,*/
 /*   PROCS: SHEWHART                                            */
 /*    DATA:                                                     */
 /*                                                              */
 /*     REF: Quesenberry, C. P. (1991). "SPC Q Charts For Start- */
 /*          Up Processes and Short or Long Runs"  Journal of    */
 /*          Quality Technology, Vol. 23, No. 3, pp. 213-224.    */
 /*                                                              */
 /*    NOTE: See Example 2, pg. 219 of above Reference.          */
 /*                                                              */
 /****************************************************************/
 options ps=60 ls=80 nodate;

 /***********************************************************/
 /*                                                         */
 /*  This program compares the behavior of the q-charts     */
 /*  for the 2 cases, 1) where parameters are known and     */
 /*  2) where parameters are unknown.                       */
 /*                                                         */
 /*  The dataset below has 30 observations, the first 20    */
 /*  are from a normal distribution with mean of 15 and     */
 /*  variance of .0004, in the last 10 observations the     */
 /*  mean has increased by .02 (or one standard deviation). */
 /*                                                         */
 /***********************************************************/


data sample;
   seed = 27951;
   do i = 1 to 30;
      subgrp = i;
      if ( i < 21 ) then do;
         x       = 15    + .02*rannor(seed);
         group  = 'Mean of 15   ';
         gcolor = 'yellow';
         end;
      else do;
         x       = 15.02 + .02*rannor(seed);
         group  = 'Mean of 15.02';
         gcolor = 'red';
         end;
      output;
      end;
   run;

 /****************************************/
 /*  Case I:                             */
 /*  Assume mu and sigma are known.      */
 /*  mu = 15, sigma = .02                */
 /****************************************/

data qchart1;
   set sample;
   q = ( x - 15 ) / .02;
run;

title 'Q-Chart for Process Mean (Parameters Known)';
symbol1 v=dot h=.5 c=white;
proc shewhart data=qchart1;
   irchart q*subgrp (group) /
                      mu0        = 0
                      sigma0     = 1
                      czones     = yellow
                      cframe     = gray
                      cinfill    = blue
                      llimits    = 1
                      xsymbol    = 'CL=0'
                      blockpos   = 2
                      cblockvar  = gcolor
                      ndecimal   = 0
                      nolimitslegend
                      novangle
                      nochart2;
   label q      = 'Standardized Value';
   label subgrp = 'Observation Number';
   run;

 /****************************************/
 /*  Case II:                            */
 /*  Assume mu and sigma are unknown.    */
 /****************************************/

data qchart2;
   set sample;
   retain lastx lxbar ls2r;
   if (_n_ = 1 ) then do;
      xbar = x;
      s2r  = 0;
      end;
   if (_n_ = 2 ) then do;
      xbar = .5*(lxbar + x);
      s2r  = (lastx - xbar)**2 + (x - xbar)**2;
      end;
   if (_n_ > 2 ) then do;
      xbar = ( 1 / _n_ )*( (_n_- 1 )*lxbar + x);
      s2r  = ((_n_- 2)/(_n_- 1))*ls2r + ( 1 / _n_)*(x - lxbar)**2;
      temp = sqrt( (_n_- 1 )/_n_ )*((x - lxbar)/sqrt(ls2r));
      q    = probit(probt( temp, _n_-2 ) );
      end;
   lastx = x;
   lxbar = xbar;
   ls2r  = s2r;
   run;

title 'Q-Chart for Process Mean (Parameters Unknown)';
symbol1 v=dot h=.5;
proc shewhart data=qchart2;
   irchart q*subgrp (group) /
                      mu0        = 0
                      sigma0     = 1
                      czones     = yellow
                      cinfill    = blue
                      cframe     = gray
                      llimits    = 1
                      xsymbol    = 'CL=0'
                      blockpos   = 2
                      cblockvar  = gcolor
                      ndecimal   = 0
                      nolimitslegend
                      novangle
                      nochart2;
   label q      = 'Standardized Value';
   label subgrp = 'Observation Number';
   run;

goptions reset=all;