### Control Limits for XBAR & S Chart

Control limits for XBar & S Charts are calculated as follows:

1. The subgroup average and the range for each subgroup are calculated by using the equations below, where n is the subgroup size:

2. The average range and the process average (the process average is the average of all subgroup averages) are calculated by using the equations below, where k is the total number of complete subgroups:

3. The standard deviation of each subgroup is calculated using the following formula, where n is the subgroup size:

4. The average standard deviation is calculated:

5. Then, the control limits are calculated based on constants:

Note: The values of the constants vary based on the subgroup size. Refer to the Table of Constants for the values of constants.

6. The process standard deviation is then: