## Methods for Estimating the Standard Deviation

When control limits are computed from the input data,
three methods (referred to as default, MAD and MMR) are
available for estimating
the process standard deviation .*Default Method*

The default estimate for is

where is the average of the moving ranges,
*n* is the number of consecutive individual measurements used to
compute each moving range, and
the unbiasing factor *d*_{2}(*n*) is defined
so that if the observations are normally distributed,
the expected value of *R*_{i} is

This method is described in the
*ASTM Manual on Presentation of Data and Control Chart Analysis*
(1976).
*MAD Method*

If you specify SMETHOD=MAD,
a median absolute deviation estimator is computed for ,as described by Boyles (1997).
It is computed as

where is the sample median.
*MMR Method*

If you specify SMETHOD=MMR,
a median moving range estimator is computed for .This estimator is described by Boyles (1997).
It is computed as

where is the median of the nonmissing moving ranges.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.