Intervals & Tests
The average of the subgroup ranges (R-bar statistics).
(n = constant) , OR
(n ≠ constant)
Rj is the Subgroup Range of subgroup j
m is the total number of subgroups included in the analysis
sigmax is the Process Sigma based on the Range chart
d2 is a function of n.
Note: When control limits for the X-Bar chart are defined as fixed values (such as when historical data is used to define control limits), the Average Range (R-bar) must be back calculated from these pre-defined control limits. This ensures that the control limits on the Range chart are at the same sensitivity as those on the X-Bar chart. In this case:
where d2 (available in any statistical quality control textbook) is based on the subgroup size n.
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