Example 42.3: Plotting OC Curves for Mean Charts

XCHART Statement

Example 42.3: Plotting OC Curves for Mean Charts

See SHWOC1 in the SAS/QC Sample Library

This example uses the GPLOT procedure and the DATA step function PROBNORM to plot operating characteristic (OC) curves for $\bar{X}$ charts with 3 $\sigma$ limits. An OC curve is plotted for each of the subgroup samples sizes 1, 2, 3, 4, and 16. Refer to page 226 in Montgomery (1996). Each curve plots the probability $\beta$ of not detecting a shift of magnitude $\nu \sigma$ in the process mean as a function of $\nu$ .The value of $\beta$ is computed using the following formula:

$\beta & = & P\{LCL \leq \bar{X_{i}} \leq UCL \} \ & = & \Phi (3 - \nu \sqrt{n}) - \Phi (-3 - \nu \sqrt{n}).$

The following statements compute $\beta$ (the variable BETA) as a function of $\nu$ (the variable NU). The variable NSAMPLE contains the sample size.

   data oc;
      keep beta nsample nu;
      do nsample=1, 2, 3, 4, 16;
         do j=0 to 400;
            nu=j/100;
            beta=probnorm( 3-nu*sqrt(nsample)) -
                 probnorm(-3-nu*sqrt(nsample));
            output;
            end;
         end;
      label nu  ='Shift in Population Mean (Unit=Std Dev)'
            beta='Probability of Not Detecting Shift';
   run;

The following statements use the GPLOT procedure to display the OC curves shown in Output 42.3.1:

   symbol1 v=none i=join w=2 c=red;
   symbol2 v=none i=join w=2 c=green;
   symbol3 v=none i=join w=2 c=yellow;
   symbol4 v=none i=join w=2 c=blue;
   symbol5 v=none i=join w=2 c=white;
   title1 'OC Curves for Shewhart Charts for Means';
   proc gplot data=oc;
      plot prob*t=nsample /
         frame
         legend=legend1
         vaxis=axis1
         haxis=axis2
         autovref
         autohref
         lvref = 2
         lHREF=2
         vzero
         hzero
         cframe = ligr
         cvref  = white;
      axis1 label =(r=0 a=90)
            value =(t=1 ' ')
            order =(0.0 0.2 0.4 0.6 0.8 1.0)
            minor =none
            offset=(0,0);
      axis2 order =(0 1 2 3 4)
            offset=(0,0)
            minor =(n=3);
      legend1 label=('Sample Size n:');
   run;

Output 42.3.1: OC Curves for Different Subgroup Sample Sizes

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