Chapter Contents Previous Next
 PCHART Statement

## Example 38.5: OC Curve for Chart

 See SHWPOC in the SAS/QC Sample Library

This example uses the GPLOT procedure and the OUTLIMITS= data set FAILLIM2 from the previous example to plot an OC curve for the p chart shown in Output 38.4.3.

The OC curve displays (the probability that pi lies within the control limits) as a function of p (the true proportion nonconforming). The computations are exact, assuming that the process is in control and that the number of nonconforming items (Xi) has a binomial distribution.

The value of is computed as follows:

Here, Ip(·, ·) denotes the incomplete beta function. The following DATA step computes (the variable BETA) as a function of p (the variable P):

   data ocpchart;
set faillim2;
keep beta fraction;
nucl=_limitn_*_uclp_;
nlcl=_limitn_*_lclp_;
do p=0 to 500;
fraction=p/1000;
if nucl=floor(nucl) then
probbnml(fraction,_limitn_,nucl-1);
if nlcl=0 then
else beta=probbeta(fraction,nlcl,_limitn_-nlcl+1) -
probbeta(fraction,nucl,_limitn_-nucl+1) +
if beta >= 0.001 then output;
end;
call symput('lcl', put(_lclp_,5.3));
call symput('mean',put(_p_,   5.3));
call symput('ucl', put(_uclp_,5.3));
run;


The following statements display the OC curve shown in Output 38.5.1:

   title "OC Curve for p Chart With LCL=&LCL, p0=&MEAN, and UCL=&UCL";
symbol i=j w=2 v=none c=yellow;
proc gplot data=ocpchart;
plot beta*fraction /
vaxis=axis1
haxis=axis2
frame
autovref
autohref
lvref = 2
lHREF=2
vzero
hzero
cframe = ligr
cHREF=cxfefefe
cvref  = cxfefefe;
label fraction = 'Fraction Nonconforming'
beta     = 'Beta';
run;


Output 38.5.1: OC Curve for p Chart

 Chapter Contents Previous Next Top