Average Range

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

 (n = constant) , OR

  (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:

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

Learn more about the Statistical Inference tools for understanding statistics in Six Sigma Demystified (2011, McGraw-Hill) by Paul Keller, in his online Intro. to Statistics short course (only $89) or his online Black Belt certification training course ($875).