Suppose there are m subgroups of n items each.

The following practice is described by Montgomery in the construction of a $\bar{X}-R$ chart:

Let $\bar{R}$ be the average range of the m subgroups. Then an estimate of $\sigma$ is $\bar{R}/d_2$.

What are the statistical basis for this estimator and how do we find its standard error?

Also from a practical point, is there still a use for the $\bar{X}-R$ charts since it seems relatively easy to compute a $\bar{X}-S$ chart nowadays?


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