Cpk, PPM and sigma level
What PPM is a Cpk of 1.33? What Cpk does 3.4 PPM need? Both conventions shown side by side, because the 1.5 sigma shift is why two sources disagree by a factor of ten.
Nothing you paste leaves this calculation. It is not stored, not logged and not sent anywhere else — the numbers are computed and returned, and that is all.
Short term (what Cpk actually says)
Six Sigma convention (with the 1.5σ shift)
This is where "six sigma = 3.4 PPM" comes from: Z = 6 with 1.5σ of assumed long-term drift. Without the shift, Z = 6 is 0.001 PPM.
The common values
| Cpk | Z | PPM (1 limit) | PPM (2 limits) | PPM with 1.5σ shift |
|---|---|---|---|---|
| 0.67 | 2.0 | 22,750 | 45,500 | 308,538 |
| 1.00 | 3.0 | 1,350 | 2,700 | 66,807 |
| 1.33 | 4.0 | 32 | 63 | 6,210 |
| 1.50 | 4.5 | 3.4 | 6.8 | 1,350 |
| 1.67 | 5.0 | 0.29 | 0.57 | 233 |
| 2.00 | 6.0 | 0.001 | 0.002 | 3.4 |
How this is calculated
Z = 3 × Cpk PPM = P(beyond Z) × 1,000,000 one-sided PPM = 2 × P(beyond Z) × 1,000,000 centred, two limits PPM = P(beyond Z − 1.5) × 1,000,000 Six Sigma convention
The part most people get wrong
Two conventions are in circulation and they differ by orders of magnitude. A table saying Cpk 1.33 is 63 PPM and a colleague saying it is 6,210 PPM are both right: the first is the short-term tail that follows directly from Cpk, the second assumes the process mean wanders by 1.5σ over the long run, as Six Sigma practice does. Quote which one you mean, or the number is not a number.
And all of it assumes normality and stability. These are areas under a normal curve. For a skewed characteristic the PPM figure is indicative at best, and for a process that is not in control it describes something that will not happen again — chart it first with the chart generator, then talk about capability.
Working from real measurements rather than an index? The Cp/Cpk calculator takes pasted data. Wondering how solid your Cpk is at all? See its confidence interval.
Want this to keep itself up to date?
A calculator answers for the data you pasted. A control chart answers for the data your line produced this morning — limits frozen at a baseline you locked, rules evaluated on every new reading, an alert when one trips.
Other free tools
- Cp / Cpk calculator — Paste measurements — or type a mean and a sigma — with your tolerance, and get Cp, Cpk, Pp, Ppk, the sigma level and the expected parts per million out of spec.
- Control limit calculator — Give it subgroups or individual readings and it returns the control limits for the chart, the range or sigma chart beneath it, and every constant it used to get there.
- Control chart generator — Paste a column of numbers, or rows of subgroups, and get a real control chart: limits from the data, Nelson rules 1–4 evaluated, out-of-control points marked.
- Nelson & Western Electric rules checker — Every run rule evaluated on your data, each violation named in plain English with what it usually indicates — a shift, a trend, tool wear, two machines mixed.
- Cpk confidence interval & sample size — A Cpk of 1.33 from 30 pieces has a 95% interval of roughly 0.97 to 1.69. See the uncertainty in your own number, and how many parts would settle it.
- Control chart constants — The whole table, n = 2 to 25, with the formula each constant belongs to. The same values the charts on this site are computed from.