Process capability (Cp, Cpk) calculator

Cp is the tolerance width divided by six standard deviations: (USL − LSL) ÷ 6σ. Cpk is the distance from the mean to the nearer limit divided by three standard deviations: the smaller of (USL − mean) ÷ 3σ and (mean − LSL) ÷ 3σ. For limits of 495 and 505, a mean of 501 and σ of 1, Cp = 10 ÷ 6 = 1.67 and Cpk = 4 ÷ 3 = 1.33.

Cp only compares the spread of the process with the width of the tolerance, as if the process were perfectly centered. Cpk also accounts for where the mean sits, so it drops as the process drifts toward a limit. Cp equals Cpk only when the mean is exactly in the middle of the limits; otherwise Cpk is lower.

A Cpk of 1.33 is a commonly used minimum. It is a rule of thumb rather than a universal standard, and some customers and industries set their own requirement. A Cpk of 1.00 means the process spread of plus or minus three standard deviations just reaches the nearer limit, and below 1.00 some output is expected out of spec.

Both use the same formula but a different standard deviation. Cpk uses the short-term, within-subgroup spread, and Ppk uses the overall spread of all the data, including drift and shifts over time. With pasted measurements, this calculator estimates the short-term spread from the average moving range divided by 1.128 and uses the sample standard deviation for Pp and Ppk.

Yes. With only an upper limit, Cpk is (USL − mean) ÷ 3σ; with only a lower limit, it is (mean − LSL) ÷ 3σ. Cp cannot be calculated, because it needs the full width between two limits. Leave the missing limit blank in the calculator.

The process should be stable, meaning in statistical control on a control chart, because capability predicts future output only for a stable process. The data should be roughly normal, since the expected parts per million out of spec assume a normal distribution. The measurement system should also be reliable, which a gauge R&R study checks.