Methods and formulas for estimating sigma for Xbar-R Chart

Sigma (σ ) is the standard deviation of the process. If you specify the standard deviation, then Minitab uses the historical value. Otherwise, Minitab uses one of the following methods to estimate σ from the data.

Minitab uses the range of each subgroup, , to calculate , which is an unbiased estimator of σ:

where

When the subgroup size is constant, the formula simplifies to the following:

where (Rbar) is the mean of the subgroup ranges, calculated as follows:

Notation

TermDescription
rirange for subgroup i
m number of subgroups
d2(·)value of unbiasing constant d2 that corresponds to the value specified in parentheses.
ninumber of observations in subgroup i
d3(·)value of unbiasing constant d3 that corresponds to the value specified in parentheses.
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