Cpk is a single number that answers one question: how much room is there between what my process actually does and what the drawing will accept?
It is the distance from the process mean to the nearer specification limit, divided by three sigma.
Cpk = min( (USL − mean) / 3σ , (mean − LSL) / 3σ )
A Cpk of 1.00 means the nearest limit sits exactly three sigma away. A Cpk of 2.00 means it sits six sigma away. Bigger is better, and the whole index exists so that "how good is this process?" has an answer you can put in a supplier scorecard.
What a good Cpk is
| Cpk | Nearest limit is | Defects on that side | Read as |
|---|---|---|---|
| 0.67 | 2σ away | ~22,750 ppm | Not fit to run |
| 1.00 | 3σ away | ~1,350 ppm | Making scrap routinely |
| 1.33 | 4σ away | ~32 ppm | The usual customer requirement |
| 1.67 | 5σ away | ~0.3 ppm | Safety-critical and automotive |
| 2.00 | 6σ away | ~0.001 ppm | "Six sigma", centred |
1.33 is the number most customers ask for. 1.67 is common for automotive characteristics and anything safety-critical. Below 1.00 the process is producing out-of-tolerance parts as a matter of routine, not as an accident.
The ppm figures assume the process is normal and centred, which is exactly the assumption the next section says to distrust.
Cp and Cpk are not the same thing
Cp ignores where the process sits. It only compares the width of the tolerance to the width of the process:
Cp = (USL − LSL) / 6σ
So Cp is the capability you could have if you centred the process perfectly. Cpk is the capability you actually have. Cpk can never exceed Cp, and the gap between them is pure centring error.
That gap is the most actionable thing on the whole report. A process with Cp = 1.80 and Cpk = 1.05 is not a variation problem — it is a process running off-target, and moving the mean is usually a morning's work. A process with Cp = 1.05 and Cpk = 1.02 is centred and genuinely too variable, which is a much longer and more expensive project. Same Cpk, completely different Monday.
The three ways Cpk lies to you
1. It assumes the process is stable, and does not check
This is the big one, and it is not a technicality.
Cpk is a prediction. It says: this is the proportion of parts that will fall outside tolerance if the process carries on behaving as it did while you were measuring it. That sentence is only meaningful if the process has one behaviour to carry on with.
An unstable process does not. If the mean drifted through the study, or a tool change moved it, or one shift runs differently from another, then the sigma you computed is a blend of several processes and the mean you computed is the average of several centres. The Cpk that comes out describes nothing that exists.
Establish control first, then measure capability. In that order, always. A control chart tells you whether the process has one behaviour; the capability index tells you whether that behaviour is good enough. Running the second without the first is the single most common error in capability reporting, and it always flatters the process.
2. It assumes normality, and the ppm figures depend on it entirely
Cpk itself is just arithmetic on a mean and a sigma — you can compute it for any data. The moment you convert it to a defect rate, you have assumed the distribution is normal, because the conversion is a normal-curve tail area.
Plenty of real characteristics are not normal and never will be. Anything bounded at zero — flatness, roundness, concentricity, surface finish, an impurity level — is skewed by its own physics. For those, the ppm implied by Cpk is wrong, usually optimistically on one side.
3. It is an estimate from a sample, and the sample is smaller than you think
Cpk is computed from a limited number of parts, so it carries a confidence interval, and that interval is much wider than most people expect.
Thirty pieces giving a Cpk of 1.33 has a 95% confidence interval of roughly 0.97 to 1.69. The true capability could be below 1.00. That study does not demonstrate a requirement of 1.33; it is merely consistent with it. Quoting the point estimate to a customer as if it were the answer is overstating what you know.
To pin a Cpk of 1.33 down tightly enough to prove it exceeds 1.33, you need several hundred parts. Most capability studies are far too small for the conclusions drawn from them.
Which sigma? This is where Cpk and Ppk part company
There are two defensible ways to estimate sigma and they answer different questions:
- Within-subgroup sigma — estimated from R̄/d₂ across subgroups, or from the mean moving range for individual readings. It captures only short-term, common-cause variation. This gives Cp and Cpk.
- Overall sigma — the plain sample standard deviation of every reading, which includes any drift between subgroups. This gives Pp and Ppk.
When the process shifts between subgroups the two disagree, and that gap is itself the useful result. Quoting a capability number without saying which sigma produced it is how these figures mislead. There is a whole guide on that disagreement.
How to report Cpk honestly
Four things, and it fits on one line:
- Cpk with its confidence interval, not the point estimate alone.
- Cp alongside it, so the reader can see centring error separately from variation.
- Which sigma you used — within-subgroup or overall.
- Evidence the process was stable while you measured, which means the control chart, not an assertion.
A capability report without the control chart behind it is a number with no warranty.