#### Example 9.1 Specifying Standard Values for the Process Mean and Process Standard Deviation

See MACEW2 in the SAS/QC Sample LibraryBy default, the EWMACHART statement estimates the process mean ( ) and standard deviation ( ) from the data. This is illustrated in the Getting Started section of this chapter. However, there are applications in which standard values ( and ) 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 metal clip manufacturing process (introduced in Creating EWMA Charts from Raw Data) has a mean of 15 and standard deviation of 0.2. The following statements specify these standard values:

ods graphics off;
title 'Specifying Standard Process Mean and Standard Deviation';
symbol v=dot h=0.8;
proc macontrol data=Clips1;
ewmachart Gap*Day /
mu0     = 15
sigma0  = 0.2
weight  = 0.3
xsymbol = mu0;
run;


The XSYMBOL= option specifies the label for the central line. The resulting chart is shown in Output 9.1.1.

Output 9.1.1: Specifying Standard Values with MU0= and SIGMA0= The central line and control limits are determined using and (see the equations in Table 9.3). Output 9.1.1 indicates that the process is out-of-control, since the moving averages for Day=17, Day=19, and Day=20 lie below the lower control limit.

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

data Cliplim;
length _var_ _subgrp_ _type_ \$8;
_var_    = 'Gap';
_subgrp_ = 'Day';
_type_   = 'STANDARD';
_limitn_ = 5;
_mean_   = 15;
_stddev_ = 0.2;
_weight_ = 0.3;

proc macontrol data=Clips1 limits=Cliplim;
ewmachart Gap*Day / xsymbol=mu0;
run;


The variable _WEIGHT_ is required, and its value provides the weight parameter used to compute the EWMAs. The variables _VAR_ and _SUBGRP_ are also required, and their values must match the process and subgroup-variable, respectively, specified in the EWMACHART 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 chart (not shown here) is identical to the one shown in Output 9.1.1.