Cp, Cpk, Pp and Ppk calculator
Paste your measurements, get the numbers and what they actually mean. Free, no signup, nothing leaves your browser.
Cpk to expected defect rate
A capability index maps to a predicted fraction of parts outside the limits, assuming a normal, centered process and counting both tails. Use it to translate an index into a number your team can picture. For the full reference table and the assumptions behind the prediction, see the dedicated Cpk to PPM calculator.
What Cpk actually tells you
Cpk answers one question: how many process spreads fit between the mean and the nearest specification limit. A Cpk of 1.0 means the nearest limit sits exactly three standard deviations from the mean, so roughly 0.13% of parts fall outside on that side. A Cpk of 1.33 buys four standard deviations of margin, which is why it became the default customer minimum in automotive and general manufacturing.
The index only means something when the process behind it is stable. If your measurements drift shift to shift, the single number flatters you. That is exactly what the Cpk to Ppk comparison is for: when the two diverge, look at stability before celebrating the Cpk.
Cp vs Cpk vs Pp vs Ppk
The formulas
σwithin is the pooled subgroup standard deviation, corrected with the c4 unbiasing constant (the default capability method used by Minitab). σoverall is the plain sample standard deviation of all the values, which is why Pp and Ppk capture drift between subgroups that Cp and Cpk deliberately ignore. In both, mean is the average of your measurements.
A worked example
A shaft diameter is specified at 25.00 mm with a tolerance of ±0.10, so the lower limit is 24.90 and the upper limit is 25.10. Five subgroups of five parts come off the machine. The mean of all 25 readings is 25.02 mm, and the pooled within-subgroup standard deviation, once the c4 constant has been applied, is 0.020 mm.
Read the gap between the two numbers, because that is where the information is. Cp of 1.67 says the spread would fit the tolerance comfortably. Cpk of 1.33 says the process is not sitting in the middle of it: the mean has drifted 0.02 mm high, and the upper limit is now the one that will bite. Nothing about the spread needs fixing here. Centre the process and the Cpk climbs to meet the Cp on its own.
Cpk to PPM, at a glance
Every capability index predicts a defect rate, on the assumption that the process is normal and centered and counting both tails. These are the rungs you meet in practice. The converter above will take any value in between.
| Cpk | Expected PPM | Percent outside | What it means |
|---|---|---|---|
| 0.50 | 133,614 | 13.4% | Well outside the limits, more than one part in ten |
| 0.67 | 44,431 | 4.4% | The two sigma process, still failing |
| 1.00 | 2,700 | 0.270% | Nearest limit exactly three sigma away |
| 1.10 | 967.0 | 0.097% | |
| 1.20 | 318.3 | 0.032% | |
| 1.33 | 66.1 | 0.007% | The common customer minimum |
| 1.50 | 6.8 | 6.8e-4% | |
| 1.67 | 0.545 | 5.5e-5% | Often required for safety or special characteristics |
| 2.00 | 0.002 | 2.0e-7% | The six sigma target, before any long term shift |
Two cautions on reading this table. The prediction is only as good as the normality assumption, and a skewed or bimodal process will not honour it. And these figures are the short-term picture: many automotive customers assume a 1.5 sigma long-term drift, which is why a process at Cpk 2.0 is quoted as 3.4 PPM in six sigma material rather than the far smaller number here.
How many samples do you need
Capability indices are estimates, and small samples make wide confidence intervals. With 30 values, a computed Cpk of 1.42 could plausibly sit anywhere from about 1.1 to 1.7. Treat anything under 25 values as a first look, aim for 50 or more before quoting a number to a customer, and use 100 or more readings in rational subgroups for a PPAP-grade study. More data does not fix an unstable process; it just measures it more honestly.
Frequently asked questions
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