# Average Sigma

Tools

Intervals & Tests

Hypothesis Test Of Sample Mean Example

Hypothesis Test Of Two Sample Variances Example

Hypothesis Test Of A Standard Deviation Compared To A Standard Value Example

Distributions

Area Under the Standard Normal Curve

Non-Normal Distributions in the Real World

Rayleigh Distribution for True Position

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.

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