Same data. Same specification. Two different numbers. Every quality engineer has had the conversation where a customer quotes one and the supplier quotes the other, and it ends in an argument about arithmetic rather than about the process.
The arithmetic is not in dispute. The two indices use different estimates of sigma, on purpose, because they answer different questions.
The only difference that matters
Cpk = min( USL − mean , mean − LSL ) / (3 × σ_within)
Ppk = min( USL − mean , mean − LSL ) / (3 × σ_overall)
Identical formulas. The numerators are the same. Everything hinges on the denominator.
σ_within is estimated from variation inside subgroups — R̄/d₂ on an X̄-R chart, s̄/c₄ on an X̄-s chart, or the mean moving range over d₂ for individual readings. It deliberately never looks at how much the process moved between subgroups.
σ_overall is the plain sample standard deviation of every reading you took, computed as if all of them came from one pot. It includes every bit of drift, every shift change, every tool change that happened during the study.
So:
- Cpk describes the process's capability over a short window — what it can do when nothing unusual is happening. Some people call it potential or short-term capability.
- Ppk describes what actually came out over the whole study. It is the honest performance number, and it is what your customer received.
When they agree, and when they do not
If the process is genuinely stable — one behaviour throughout, nothing but common-cause variation — then between-subgroup movement is nothing more than the sampling noise you would expect. σ_within and σ_overall converge, and Cpk ≈ Ppk.
If the process shifted, drifted, or has a systematic difference between subgroups, σ_overall picks it up and σ_within does not. σ_overall gets larger, Ppk drops below Cpk, and the size of the gap is a measurement of how much the process moved during the study.
That is the entire diagnostic:
| What you see | What it means | What to do |
|---|---|---|
| Cpk ≈ Ppk, both high | Stable and capable | Nothing. Keep charting. |
| Cpk ≈ Ppk, both low | Stable and genuinely too variable | Variation reduction. Long project. |
| Cpk ≫ Ppk | The process is capable of better than it delivered — something moved | Find the special cause. This is the cheap win. |
| Ppk > Cpk | Almost always an artefact of small samples or bad subgrouping | Check how you subgrouped |
Cpk ≫ Ppk is good news, correctly read. It says the machine can hold the tolerance and something is knocking it off — a setup, a tool change, a batch of material, one shift doing it differently. That something is findable and usually fixable, and fixing it moves Ppk up towards Cpk without touching the process capability at all. It is far cheaper than a variation-reduction project.
The mistake is treating the gap as a reporting inconvenience — picking whichever index looks better, or averaging them, or arguing that the customer asked for the wrong one. The gap is the finding.
Ppk larger than Cpk means you subgrouped badly
Mathematically Ppk can exceed Cpk, and when it does it is nearly always telling you the subgroups are wrong.
The usual cause: you subgrouped across the very thing that varies. Take one part from each of four spindles as a subgroup of four, and spindle-to-spindle difference is now inside the subgroup. It inflates R̄, which inflates σ_within, which deflates Cpk — while σ_overall, which does not care how you grouped anything, stays put.
A subgroup should be parts made under conditions as nearly identical as you can arrange: consecutive pieces, one machine, one operator, one setup. Get that wrong and every index computed from the chart is wrong with it.
AIAG's convention, and why it exists
The AIAG PPAP convention is worth knowing because it is what most automotive customers actually ask for:
- Ppk for a preliminary study, on a short production run, before the process has demonstrated stability. You have no basis for claiming a short-term sigma yet, so you report what actually happened. The bar is usually Ppk ≥ 1.67.
- Cpk for ongoing capability, once the process is in statistical control and you have a control chart proving it. The bar is usually Cpk ≥ 1.33.
The logic is consistent: you may only quote Cpk once you have earned it. Cpk is a claim about a process that has one behaviour, and the control chart is the evidence that it does. Reporting Cpk on an unstable process is quoting a prediction whose precondition you never checked — and it always flatters, because σ_within excludes exactly the movement that hurt you.
What to do with both numbers
Report them together, always, with the chart behind them:
- Ppk — what the customer actually received.
- Cpk — what the process is capable of.
- The gap — how much was lost to instability, in capability units.
- The control chart — the evidence for whether Cpk was legitimate to quote.
If someone shows you a capability report with one index, no chart, and no confidence interval, you have not been told whether the process is any good. You have been told a number.