Methods for Estimating the Standard Deviation
When control limits are determined from the input data, two
methods (referred to as default and MVLUE) are available
for estimating .
The default estimate for is
where N is the number of subgroups for which
Ri is the sample range of the observations
xi1, . . . , in the
i th subgroup.
A subgroup range Ri is included in the calculation
only if .The unbiasing factor d2(ni) is defined
so that, if the observations are normally distributed,
the expected value of Ri is .Thus, is the unweighted average of N unbiased
estimates of .This method is described in the ASTM Manual on Presentation of
Data and Control Chart Analysis (1976).
If you specify SMETHOD=MVLUE,
a minimum variance linear unbiased estimate (MVLUE) is computed for
. Refer to Burr (1969, 1976) and Nelson (1989, 1994).
The MVLUE is a weighted average of N unbiased estimates
of of the form Ri/d2(ni), and it is computed as
fi = [([d2(ni)]2)/([d3(ni)]2)]
A subgroup range Ri is included in the calculation only
if , and N is the number of subgroups
for which . The unbiasing factor d3(ni) is defined
so that, if the observations are normally distributed, the expected
value of is .The MVLUE assigns greater weight to estimates of from
subgroups with larger sample sizes, and it is intended for
situations where the subgroup sample sizes vary. If the subgroup
sample sizes are constant, the MVLUE reduces to the default
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