Standardizing Differences from Nominal

Specialized Control Charts

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 $\pm3$ .

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;

   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_ ;

   proc sort data=new;
      by sample;

   symbol v=dot c=yellow;
   title 'Standardized Chart';
   proc shewhart data=new;
      irchart z*sample (prodtype) /
         blocklabtype  = scaled
         mu0           = 0
         sigma0        = 1
         split         = '/'
         cframe        = vigb
         cinfill       = vlib
         cconnect      = yellow;
      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 49.23.

Figure 49.23: Standardized Difference Chart

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