Quality & Compliance
Cp and Cpk: Reading Process Capability Numbers
The short answer
Cp measures whether a process is precise enough to fit inside your tolerance band. Cpk measures whether it is also centered within it. A Cpk of 1.33 is the usual minimum for production and corresponds to roughly 63 defective parts per million. A high Cp with a low Cpk means the process is capable but off center, which is normally an adjustment rather than a new machine. That distinction is the most useful thing these numbers give a buyer.
Cp and Cpk in one worked example
Take a bore specified at 20.00 mm plus or minus 0.05, so the tolerance band is 0.10 mm wide. A shop runs 100 parts and measures them. The spread of the process, six standard deviations, comes out at 0.06 mm.
Cp compares the tolerance width to the process spread: 0.10 divided by 0.06 gives Cp of 1.67. The process is comfortably narrow enough to fit inside your tolerance.
Now suppose the bores average 20.03 mm rather than 20.00. The process is still just as narrow, so Cp is unchanged at 1.67. But it is sitting close to the upper limit, and Cpk measures the distance from the process mean to the nearest limit instead of to both. That distance is 0.02 mm against three standard deviations of 0.03, giving Cpk of 0.67.
Same process, same machine, same operator. Cp says capable, Cpk says you are about to make bad parts. Cpk is the honest number because parts do not fail against the center of your tolerance, they fail against its edges.
What the numbers mean in defect rates
Capability indices are only useful if you can translate them into parts. The table below assumes a centered, normally distributed process, which is a real assumption and one worth remembering when a number looks too good.
The practical thresholds are 1.33 and 1.67. Below 1.33 the process needs sorting or improvement. Above 1.67 you are paying for capability you may not need.
| Cpk | Process spread vs tolerance | Defects per million | Typical interpretation |
|---|---|---|---|
| 0.67 | Process wider than tolerance | About 45,000 | Not capable. Sorting or 100 percent inspection required |
| 1.00 | Process exactly fills tolerance | About 2,700 | Marginal. Any drift produces scrap immediately |
| 1.33 | Tolerance 33 percent wider than process | About 63 | Common minimum for ongoing production |
| 1.67 | Tolerance 67 percent wider than process | About 0.6 | Common requirement for critical characteristics |
| 2.00 | Tolerance double the process spread | About 0.002 | Six sigma. Rarely required, expensive to achieve |
High Cp with low Cpk is a centering problem
This is the pattern worth recognizing, because it changes what you should ask for. Cp and Cpk are equal only when the process is perfectly centered. The gap between them measures how far off center it is running.
A centering problem is usually cheap to fix. It is a tool offset, a fixture adjustment, a compensation for tool wear. A spread problem is expensive, because it means the machine, the fixturing, the tooling or the material variation cannot hold what you asked for, and fixing it means changing one of those things.
So when a capability study comes back poor, the first question is not can you do better. It is what are Cp and Cpk separately.
| Cp | Cpk | Diagnosis | Usual fix |
|---|---|---|---|
| High | High | Capable and centered | Nothing. Monitor per the control plan |
| High | Low | Capable but off center | Offset adjustment or compensation. Usually quick and cheap |
| Low | Low | Process spread too wide for the tolerance | Different process, better fixturing, or open the tolerance |
| Low | High | Not possible | Cpk cannot exceed Cp. Check the data or the calculation |
Where Cpk shows up in a PPAP
Capability studies are element 9 of a PPAP submission, and they are normally required only on characteristics designated as special, critical or key. That designation comes from you, on the drawing.
This matters more than it sounds. If you mark thirty characteristics as critical, you have asked for thirty capability studies, each requiring a run of parts and a measurement system that has itself been validated. If you mark the four that actually determine whether the part works, you get meaningful data on the things that matter and a far cheaper, faster submission.
Over designation of critical characteristics is one of the most reliable ways to make a PPAP expensive without making a part better.
The capability cliff when you tighten a tolerance
Capability is not linear in tolerance, and this is the part that catches designers out.
Go back to the bore with a process spread of 0.06 mm. At plus or minus 0.05 the Cp is 1.67 and everything is fine. Tighten to plus or minus 0.035 and the band is 0.07, so Cp falls to 1.17: the same process is now marginal. Tighten to plus or minus 0.025 and Cp is 0.83, meaning the process now produces scrap continuously and the shop has to move to a different operation, add a grinding pass, or inspect every part.
A 50 percent tolerance reduction did not raise the price 50 percent. It changed the process. That step change is why a tolerance you added for comfort can double a price, and why the useful question to a shop is which tolerance is driving the operation rather than can you hold this.
Cpk against Ppk, and why the distinction is not pedantic
Cpk is calculated from the within subgroup variation of a process that has been demonstrated to be stable. Ppk uses the total variation across the whole study, stable or not.
On a new process at PPAP time you will normally be given Ppk, because a process running for the first time has not yet demonstrated stability over time. Ppk is the more conservative and more honest number for a launch. Cpk becomes meaningful once the process has been running long enough for control charts to show it is predictable.
If a supplier reports a high Cpk on a brand new process, ask how stability was established. The number is not wrong so much as it is answering a question nobody asked yet.
What this costs you
Capability requirements have a price, and it is mostly in inspection and process choice rather than in a line item labeled quality.
A requirement of Cpk 1.33 on a handful of characteristics is normal and cheap. A requirement of 1.67 on the same characteristics often pushes the shop to a tighter process, a better machine or an added operation, and the quote moves accordingly. A requirement of 1.67 on twenty characteristics can change which shops will bid at all.
The study itself also costs. It needs a run of parts, typically thirty or more consecutive pieces, plus a measurement system analysis proving the gauge can resolve the variation being measured. On a low volume part the capability study can cost more than the parts.
Which is the argument for designating few critical characteristics and setting the requirement at the level the application genuinely needs.
What to send, and what to ask
Send a drawing where critical characteristics are explicitly marked and everything else is left at general tolerance. Say what the tight dimensions are for, because a shop that knows a bore is a bearing fit can propose a fit callout instead of a tighter number.
Then ask for Cp and Cpk separately rather than a single capability figure. Ask which measurement system was used and whether an MSA was performed, since a gauge that cannot resolve the variation makes any capability number meaningless. Ask whether the figure is Cpk or Ppk and over how many parts. And on anything reported below 1.33, ask whether the limitation is spread or centering, because the answer tells you whether this is an adjustment or a process change.
A shop that answers those four clearly is telling you it actually measures its own processes, which is more informative than the numbers themselves.