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Cpk Calculator: Process Capability (Cp, Cpk, PPM)
Cp, Cpk and the PPM out of spec.
Marginal: inside spec at 3σ, no margin for drift. Centring the mean raises Cpk toward 1.39.
The spec window and the process
Do this Center the mean at 10.00 (from 10.01): Cpk 1.11 to 1.39.
The Cpk formula
Cp = (USL − LSL) / 6σ. PPM out of spec is the area of the normal curve beyond each limit, times 1,000,000.
How to use this calculator
- Enter the spec limits USL and LSL. Leave one blank for a one-sided spec.
- Enter the mean and standard deviation or paste the measurements, one per line or comma separated.
- Read the result Cp, Cpk, PPM out of spec and yield update as you type.
What Cp and Cpk measure
Both compare the voice of the customer (the spec limits) with the voice of the process (its spread). Cp asks whether the process spread would fit inside the spec if it were perfectly centred. Cpk asks how close the process actually sits to the nearer limit. A process with Cp 2.0 and Cpk 0.8 is precise but off target: re-centre it and Cpk rises toward 2.0 without reducing any variation.
Worked example
A bore is specified at 10.00 ± 0.05 mm, so USL = 10.05 and LSL = 9.95. A stable process runs at a mean of 10.01 mm with a within-subgroup σ of 0.012 mm.
Cpu = (10.05 − 10.01) / (3 × 0.012) = 0.04 / 0.036 = 1.11
Cpl = (10.01 − 9.95) / (3 × 0.012) = 0.06 / 0.036 = 1.67
Cpk = min(1.11, 1.67) = 1.11
PPM above USL: z = 0.04 / 0.012 = 3.33, tail = 429 PPM. Below LSL: z = 5.0, tail = 0.3 PPM.
Cp of 1.39 says the spread fits. Cpk of 1.11 says the mean sits 0.01 mm high, which costs about 429 PPM on the upper side. Re-centring to 10.00 gives Cpk = Cp = 1.39 and about 31 PPM in total. These are the numbers loaded in the calculator above.
Reading the result
| Cpk | Nearest limit at | PPM, that side (normal) | Typical reading |
|---|---|---|---|
| 0.67 | 2σ | 22,750 | Not capable: sort or fix |
| 1.00 | 3σ | 1,350 | Barely capable, no margin for drift |
| 1.33 | 4σ | 32 | Common minimum requirement |
| 1.67 | 5σ | 0.3 | Common requirement for critical characteristics |
| 2.00 | 6σ | 0.001 | Six Sigma short-term capability |
Before you trust the number
- Stable first. Capability only predicts a process that is in statistical control. Check a control chart before computing Cpk.
- Enough data. 25 subgroups or about 100 readings is a common minimum. Cpk from 20 parts has a wide confidence interval.
- Measurement system. If gauge variation is a large share of the tolerance, part of the σ is the gauge. Run a gauge R&R first.
- Normal data. The PPM figures assume normality. Look at a histogram.
To convert a defect count into a sigma level instead, use the DPMO calculator. The process capability guide covers Pp, Ppk and how to estimate within-subgroup σ from R-bar.
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Frequently asked questions
What is a good Cpk?
A common minimum is 1.33, which puts the nearest spec limit 4 standard deviations from the mean (about 32 PPM out of spec on that side, if the process is normal and stable). Many automotive and aerospace customers ask for 1.67 on critical characteristics. Below 1.0 the process makes out-of-spec parts as a matter of course.
What is the difference between Cp and Cpk?
Cp compares the spec width to the process spread and ignores where the process is centred: Cp = (USL - LSL) / 6 sigma. Cpk also accounts for centring: it is the distance from the mean to the nearer limit, divided by 3 sigma. Cp is what the process could do if centred; Cpk is what it does. They are equal only when the process is centred.
What is the difference between Cpk and Ppk?
Same formula, different sigma. Cpk uses within-subgroup (short-term) variation, usually estimated from a control chart as R-bar / d2. Ppk uses the overall standard deviation of all the data, which includes shifts between subgroups. If you paste raw data here, the result is Pp and Ppk. Enter a within-subgroup sigma to get Cp and Cpk.
How do I calculate Cpk with only one spec limit?
Leave the other limit blank. Cpk is then the one-sided index: (USL - mean) / 3 sigma for an upper limit only, or (mean - LSL) / 3 sigma for a lower limit only. Cp is not defined without both limits.
Does Cpk work if the data is not normal?
The index can be computed, but the PPM estimate from it assumes a normal distribution. Skewed characteristics such as flatness, runout or concentricity often need a non-normal method or a transformation. Check a histogram first, and check the process is in statistical control on a control chart, or the index predicts nothing.
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