Average Range

The average of the subgroup ranges (R-bar statistics).

$images\ebx_894160647.jpg$ (n = constant) , OR

$images\conc0099_wmf.jpg$ (n ≠ constant)

where:

Rj is the Subgroup Range of subgroup j

m is the total number of subgroups included in the analysis

sigma_x 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:

$images\conc0100_wmf.jpg$

where d2 (available in any statistical quality control textbook) is based on the subgroup size n.