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 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 charts with 3 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 of not detecting a shift of magnitude in the process mean as a function of .The value of is computed using the following formula:

The following statements compute (the variable BETA) as a function of (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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