### Control Limits for X Tilde & R Charts

Control limits for XBar & R 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. To calculate the control limits, first the average of the subgroup medians and the average of the subgroup ranges are calculated. Then, the control limits are calculated using constants based on subgroup size (Refer to the Table of Constants):

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

4. The process standard deviation is then: