Calculate Cpk and Cp from specification limits, process mean and standard deviation, with expected ppm out of spec, or find the maximum sigma for a target Cpk.

Compare the process location and spread with specification limits.

Within-subgroup standard deviation gives Cpk. Enter the overall standard deviation instead to get Ppk.

Optional settings
Blank uses 1.33 as a comparison assumption, not a universal acceptance rule.

CPK Formula

The following formula is used to calculate the CPK, or process capability index, of a given set of data.

Cpk = min[(USL − mean) / (3 × sigma), (mean − LSL) / (3 × sigma)]
  • Where CPK is the process capability index
  • USL is the upper limit
  • LSL is the lower limit
  • std is the standard deviation

Subtract the mean from USL and LSL from the mean, divide each difference by (3 × within-process sigma), and take the smaller result. Cp = (USL − LSL)/(6 × sigma). One-sided specifications use Cpu or Cpl. To find maximum sigma for a positive target, divide the nearest limit distance by (3 × target); the mean must lie strictly inside the applicable limits.

CPK Definition

Cpk compares process location and within-process spread with specification limits. Conventional interpretation assumes a stable process and a suitable normal model; the calculator does not verify either assumption. Benchmarks are user requirements, not universal acceptance rules.

Example Problem

How to calculate CPK?

The first step in calculating CPK (process capability index) is determining the upper and lower limits of the specifications. In this example, we are looking at a product that needs to be made to certain specifications. The upper limit of one of the dimensions on that product is 5 inches, and the lower limit is 4 inches.

Next, determine the mean of the data. This will be the mean of the dimension through a certain lot of goods. In this case, after 1000 items are produced, the mean is found to be 4.75 inches.

For this example, assume the within-process standard deviation is 0.3 inches. An overall sample standard deviation is not automatically the within-process estimate.

Finally, calculate the process capability index using the formula above:

Cpk = min[(USL − mean) / (3 × sigma), (mean − LSL) / (3 × sigma)]

Cpk ≈ 0.277778

FAQ

What is CPK?

CPK is a term that stands for process capability index. The process capability index is a value used to measure the ability of a process to produce to a customer’s specifications.

How do you improve CPK?

Improve capability by reducing within-process variation and centering the mean between fixed specification limits. Moving limits closer to the mean would reduce capability.