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.

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.

Questions people ask about this

What PPM is a Cpk of 1.33?

About 32 PPM beyond the nearest specification limit, or 63 PPM for a centred process with two limits. Under the Six Sigma convention, which assumes the mean drifts 1.5 sigma over the long term, the same Cpk is quoted as roughly 6,210 PPM. Both are correct; they answer different questions.

How do you convert Cpk to sigma level?

Sigma level (Z) is simply 3 × Cpk. A Cpk of 1.33 is 4 sigma, 1.67 is 5 sigma, and 2.00 is 6 sigma. The conversion in the other direction is Cpk = Z / 3.

Why is six sigma 3.4 PPM and not 0.001 PPM?

Because the 3.4 figure includes an assumed 1.5 sigma long-term shift in the process mean. Without that shift, six sigma is about 0.001 PPM. This is the single most common source of confusion when two sources quote wildly different defect rates for the same capability index.

Does this assume a normal distribution?

Yes. Every PPM figure here is an area under a normal curve. For a skewed characteristic — flatness, roundness, anything bounded at zero — treat the result as indicative, and for a process that is not in control it describes something that will not happen again.

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.

Start now See it on live data

More capability 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.
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.

Everything else

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.
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.
X̄-R chart calculator — Subgroups in, X̄ and R charts out — limits from A₂, D₃ and D₄, run rules evaluated, and the range chart shown first because it decides whether the averages chart can be trusted.
X̄-s chart calculator — For subgroups big enough that the range wastes them. Limits from A₃, B₃ and B₄, sigma recovered with the c₄ correction, and the s chart read first because it decides whether the averages chart can be trusted.
I-MR chart calculator — For processes that give you one number at a time — a batch, an oven, a destructive test. Limits from the mean moving range, run rules evaluated, and an honest note about what an individuals chart cannot see.
Levey-Jennings chart with Westgard rules — Paste your QC results with the assigned mean and SD from the package insert, and get the chart with every sigma band drawn and all six Westgard rules evaluated — each one named, and labelled random or systematic error.
Bland-Altman plot — Paired readings from two methods, plotted as difference against average — with the bias, the limits of agreement, their confidence intervals, and a test for whether the disagreement depends on the magnitude.
Pareto chart generator — Categories and counts in, ranked bars and the cumulative line out — with the vital few named, an "Other" bucket that always sorts last, and an honest warning when the distribution is flat and there is no dominant cause to attack.
Box and whisker plot generator — One column per group, boxes side by side. Quartiles, the 1.5×IQR fences, whiskers that stop at real readings and outliers drawn individually — with the quartile method stated, because that is why your plot and Excel's disagree.
Histogram and normality test — A histogram with the fitted normal curve, both standard bin rules with a reasoned recommendation, and an Anderson-Darling test that refuses to tell you your data is normal — because no test can.
Gage R&R calculator (ANOVA) — Paste a crossed study — part, operator, reading — and get the full ANOVA: repeatability and reproducibility separated, the part-by-operator interaction tested rather than assumed away, %GRR, %Tolerance and ndc against AIAG's bands.
p, np, u and c chart calculator — Counted data rather than measured: proportion defective, number defective, defects per unit. Limits that step with the sample size instead of pretending it never changed, and an honest warning when the counts are too low for three-sigma limits to mean anything.
Grubbs outlier test — The G statistic against its critical value, the p-value, and the point implicated — plus a straight answer about what to do next, which is almost never to delete the reading.
Scatter diagram and correlation — Paired readings plotted, with Pearson r, Spearman rho, r², the least-squares line and its p-value — and the two reported together, because when they disagree the disagreement is the finding.
Standard deviation calculator — The usual summary statistics, and the thing a spreadsheet will not tell you: the within-subgroup sigma a control chart uses, beside the overall sigma a textbook means. The gap between them is why Cpk and Ppk disagree.