Example 17.39 Specifying Standard Values for the Process Mean and Standard Deviation

See SHWXR3 in the SAS/QC Sample LibraryBy default, the XRCHART statement estimates the process mean ( $\mu$ ) and standard deviation ( $\sigma$ ) from the data, as in the previous example. However, there are applications in which standard values ( $\mu _0$ and $\sigma _0$ ) are available based, for instance, on previous experience or extensive sampling. You can specify these values with the MU0= and SIGMA0= options.

For example, suppose it is known that the adhesive coating process introduced in the previous example has a mean of 1260 and standard deviation of 15. The following statements specify these standard values:

ods graphics off;
title 'Specifying Standard Process Mean and Standard Deviation';
proc shewhart history=Tape;
   xrchart Weight*Sample / mu0     = 1260
                           sigma0  = 15
                           xsymbol = mu0;
run;

The XSYMBOL= option specifies the label for the central line on the $\bar{X}$ chart. The resulting $\bar{X}$ and R charts are shown in Output 17.39.1.

Output 17.39.1: Specifying Standard Values with MU0= and SIGMA0=

The central lines and control limits for both charts are determined by using $\mu _0$ and $\sigma _0$ (see the equations in Table 17.72). Output 17.39.1 indicates that the process is in statistical control.

You can also specify $\mu _0$ and $\sigma _0$ with the variables _MEAN_ and _STDDEV_ in a LIMITS= data set, as illustrated by the following statements:

data Tapelim;
   length _var_ _subgrp_ _type_ $8;
   _var_    = 'Weight';
   _subgrp_ = 'Sample';
   _type_   = 'STANDARD';
   _limitn_ = 5;
   _mean_   = 1260;
   _stddev_ = 15;

proc shewhart history=Tape limits=Tapelim;
   xrchart Weight*Sample / xsymbol=mu0;
run;

The variables _VAR_ and _SUBGRP_ are required, and their values must match the process and subgroup-variable, respectively, specified in the XRCHART statement. The bookkeeping variable _TYPE_ is not required, but it is recommended to indicate that the variables _MEAN_ and _STDDEV_ provide standard values rather than estimated values.

The resulting charts (not shown here) are identical to those shown in Output 17.39.1.

XRCHART Statement: SHEWHART Procedure

Example 17.39 Specifying Standard Values for the Process Mean and Standard Deviation