IRCHART Statement: SHEWHART Procedure
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, 
is the number of consecutive individual measurements used to compute each moving range, and the unbiasing factor 
is defined so that if the observations are normally distributed, the expected value of 
is
 |
This method is described in the American Society for Testing and Materials (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.