Standardizing Differences from Nominal :: SAS/QC(R) 12.3 User's Guide

Standardizing Differences from Nominal

When the variances across product types are not constant, various authors recommend standardizing the differences from nominal and displaying them on a common chart with control limits at $\pm 3$ .

To illustrate this method, assume that the hypothesis of homogeneity is rejected for the differences in Old. Then you can use the product-specific estimates of $\sigma$ in Baselim to standardize the differences from nominal in New and create the standardized chart as follows:

proc sort data=new;
   by Prodtype;
run;

data new;
   keep Sample Prodtype z Diff Diameter Nominal _stddev_;
   label Sample = 'Sample Number';
   format Diff 5.2 ;
   merge Baselim new(in = a);
      by Prodtype;
   if a;
   z = (Diameter - Nominal) / _stddev_ ;
run;

proc sort data=new;
   by Sample;
run;

title 'Standardized Chart';
proc shewhart data=new;
   irchart z*Sample (Prodtype) /
      blocklabtype  = scaled
      mu0           = 0
      sigma0        = 1
      split         = '/';
   label Prodtype = 'Product Classification'
         z = 'Standardized Difference/Moving Range';
run;

Note that the options MU0= and SIGMA= specify that the control limits for the standardized differences from nominal are to be based on the parameters $\mu =0$ and $\sigma =1$ . The chart is displayed in Figure 17.213.

Figure 17.213: Standardized Difference Chart