### Capability Indexes: Table of Calculations

Calculations of capability indexes vary based on the control chart selected and the subgroup size:

If the subgroup's size is greater than 1:
| XBar & R | X Tilde & R | XBar & S
Cp | `((USL - LSL))/(6sigma_R)` | `((USL - LSL))/(6sigma_R)` | `((USL - LSL))/(6sigma_S)`
Cpu | `((USL - mu))/(3sigma_R)` | `((USL - mu))/(3sigma_R)` | `((USL - mu))/(3sigma_S)`
Cpl | `((mu - LSL))/(3sigma_R)` | `((mu - LSL))/(3sigma_R)` | `((mu - LSL))/(3sigma_S)`
Cpk | `M\i\n(Cpu,Cpl)`* | `M\i\n(Cpu,Cpl)`* | `M\i\n(Cpu,Cpl)`*

* If there is no lower tolerance, then `Cpk = Cpu`.

If the subgroup's size is 1:
| RX | XMR(2) | XMR(3)
Cp | `((USL - LSL))/(6sigma_(PR))` | `((USL - LSL))/(6sigma_(MR2))` | `((USL - LSL))/(6sigma_(MR3))`
Cpu | `((USL - mu))/(3sigma_(PR))` | `((USL - mu))/(3sigma_(MR2))` | `((USL - mu))/(3sigma_(MR3))`
Cpl | `((mu - LSL))/(3sigma_(PR))` | `((mu - LSL))/(3sigma_(MR2))` | `((mu - LSL))/(3sigma_(MR2))`
Cpk | `M\i\n(Cpu,Cpl)`* | `M\i\n(Cpu,Cpl)`* | `M\i\n(Cpu,Cpl)`*

* If there is no lower tolerance, then `Cpk = Cpu`.

See also:

Calculation of Capability Based on Normal Distribution Parameters

Estimates of Standard Deviation Based on Control Charts