Average Sigma
The average of the subgroup sigma (S-Bar).
(n = constant) , OR
(n ≠ constant)
where:
Sj is the Subgroup Sigma of subgroup j
m is the total number of subgroups included in the analysis
sigma-x is the Process Sigma based on the Sigma chart
c4 is a function of n (available in any statistical quality control textbook)
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 Sigma (S-bar) must be back calculated from these pre-defined control limits. This ensures that the control limits on the Sigma chart are at the same sensitivity as those on the X-Bar chart. In this case:
where c4 (available in any statistical quality control textbook) is based on the subgroup size n.