Example 20.2: Displaying Limits Based on Asymptotic Values

EWMACHART Statement

Example 20.2: Displaying Limits Based on Asymptotic Values

See MACEW3 in the SAS/QC Sample Library

The upper (lower) control limits in Output 20.1.1 are monotonically increasing (decreasing). As the number of subgroups increases, the control limits approach the following asymptotic values:

${\rm LCL} = \overline{\overline{X}}-k\hat{\sigma}\sqrt{r/n(2-r) }$

${\rm UCL} = \overline{\overline{X}}+k\hat{\sigma}\sqrt{r/n(2-r) }$

These constant limits are displayed if you specify the ASYMPTOTIC option, as illustrated by the following statements:

   title 'Constant Control Limits Based on Asymptotic Values';
   symbol v=dot c=salmon;
   proc macontrol data=clips1;
      ewmachart gap*day /
          mu0      = 15
          sigma0   = 0.2
          weight   = 0.3
          xsymbol  = mu0
          asymptotic
          cframe   = vibg
          cinfill  = ligr
          coutfill = yellow
          cconnect = salmon;
    run;

The chart is shown in Output 20.2.1.

Output 20.2.1: Asymptotic Control Limits

Note that the same three points that were outside the exact limits (displayed in Output 20.1.1) fall outside the asymptotic limits. The exact limits quickly approach the asymptotic values, so only the first few subgroups have appreciably different limits.

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