Cpk calculator: is your process capable? Cp, Pp and Ppk from measurements
Paste the measurements in the order they were taken, enter the upper and lower tolerance limits (USL and LSL) and get Cp, Cpk, Pp and Ppk, and for Cpk and Ppk a confidence interval. The scale says whether the process is capable, marginal or incapable.
Opens without an account 3 times a day. A free account removes the limit.
- 4 indicesCp, Cpk, Pp and Ppk
- 2 sigmasshort-term and long-term
- Interval for Cpk and Ppkconfidence, at 90, 95 or 99 %
- Scale1.33 and 1.67
Cpk calculator: what process capability is
This Cpk calculator is a free online tool from EduFacturing that takes a list of measurements and tolerance limits, calculates Cp, Cpk, Pp and Ppk, and says whether the process is capable. It is capable at a Cpk of 1.67 or more, marginal from 1.33, incapable below 1.33.
Measurements go one per line, in the order they were taken, with a point or a comma as the decimal mark. The ten sample diameters between 9.97 and 10.04 mm with a tolerance of 9.90 to 10.10 give Cp 1.13 and Cpk 1.05.
Everything is calculated in the browser: the measurements are not sent anywhere.
Cp, Cpk, Pp and Ppk from measurements
Calculates Cp, Cpk, Pp and Ppk with two sigmas
Cp and Cpk use the short-term sigma from the moving range, and Pp and Ppk the long-term sample sigma. Below them sit the mean, both sigmas and the number of measurements.
Rates: capable, marginal or incapable
Cpk and Ppk are capable from 1.67, marginal from 1.33 and incapable below 1.33. With one limit only Cpk and Ppk show, and an upper limit not above the lower raises a warning.
Gives a confidence interval for Cpk and Ppk
The interval is at 90, 95 or 99 % and is indicative. For the ten sample measurements, Cpk 1.05 lies between 0.52 and 1.58 at 95 %.
Reads the measurements carefully
It accepts a decimal comma and a point. Entries like 10,02,10,05 are not guessed at: they are left out and listed, and non-numbers are counted. Under 30 measurements a small-sample warning shows.
When you need a Cpk calculator
Capability is measured on parts already measured and says how the process behaved.
Checking a dimension in printing or milling
Measure ten consecutive parts on a critical dimension and see whether the process holds the tolerance on the drawing.
Centering or spread
A high Cp with a low Cpk means a stable process shifted toward a limit: center the setting. A Cpk well above Ppk means drift between groups.
A customer requirement
A customer asks for a Cpk of at least 1.33. Compare with the lower bound of the interval, not only the point estimate.
How Cpk is calculated
Two sigmas give two pairs of indices. Cp and Cpk use the short-term sigma, Pp and Ppk the long-term one, so for the same data the numbers differ.
Moving range
The range is the absolute difference between each measurement and the one before. That is why order matters and the input is never sorted.
Two sigmas
The within-group sigma is the mean range divided by 1.128. The overall sigma is the standard deviation with n − 1 in the denominator.
Indices
Cp is the tolerance width against six sigmas. Cpk takes the nearer limit, and Pp and Ppk are the same with the overall sigma.
Verdict
Cpk is compared with 1.33 and 1.67, and the interval shows how firm the number is at this sample size.
| Applies to | Formula | Meaning |
|---|---|---|
| Within-group σ | σ = R̄ / 1.128 | R̄ is the mean of |x_i − x_(i−1)| |
| Cp | Cp = (USL − LSL) / (6σ) | Pp is the same with the overall σ |
| Cpk | Cpk = min[(USL − x̄) / 3σ; (x̄ − LSL) / 3σ] | with one limit only one term remains |
| Interval | Cpk ± z · √(1 / (9n) + Cpk² / (2(n − 1))) | z is 1.645, 1.96 or 2.576 for 90, 95 or 99 % |
| Scale | Cpk ≥ 1.67 capable; 1.33 to 1.67 marginal; below 1.33 incapable | an AIAG SPC convention, not a law |
What is different here
An interval beside the number
With ten measurements, Cpk 1.05 lies between 0.52 and 1.58. The tool shows the interval and warns under 30 measurements instead of leaving one bare number.
No false Cp
With one limit Cp is absent, not calculated with zero or infinity. A decimal mark is not guessed in an ambiguous entry.
The tool assumes roughly normal data and one unchanged process: one machine, one material, one setting. Measurements from different machines should not be mixed, and skewed data, such as roundness, needs other indices that are not calculated here.
The interval uses the approximate Bissell (1990) formula and is indicative. For formal approval (PPAP, MSA) a validated method and usually 25 to 30 consecutive measurements are needed.
Questions about Cpk and process capability
What is Cpk and how is it calculated?
Cpk is a process capability index: it takes the nearer limit and measures it in three sigmas, Cpk = min[(USL − x̄) / 3σ; (x̄ − LSL) / 3σ]. With one limit only one term remains.
What is the difference between Cp and Cpk?
Cp compares the width of the tolerance with the spread of the process and knows nothing about centering. Cpk takes the nearer limit, so it penalizes both spread and shift.
What is a good Cpk value?
The tool says capable from 1.67 and marginal from 1.33. That is an industry convention, and a customer may ask for more. At a Cpk of 1.0 the limit sits at three sigmas, and a centered normal process gives about 0.27 % defects.
Why do Cp and Pp differ?
Cp measures short-term noise between neighboring parts, and Pp the whole spread, including slow drift. A large gap between the two pairs means the process is moving, not that the sum is wrong.
Does the order of the measurements matter?
Yes. In the example with sorted numbers the within-group sigma falls from 0.0296 to 0.0069 and Cpk jumps from 1.05 to 4.50. Sorted data makes a process look falsely calm.
How many measurements do I need for Cpk?
Ten give a rough estimate: Cpk 1.05 lies between 0.52 and 1.58. Under 30 measurements the tool warns, and to confirm a process one usually takes 25 to 30 consecutive ones.
Is the Cpk calculator free?
Yes. Without an account it opens 3 times a day. With a free account there is no limit.
The Cp/Cpk calculator is free. Pro opens the rest
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Calculate your process capability
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