Cp, Cpk, Pp, and Ppk are four capability indices that answer two questions at once: is the process capable in potential or in actual performance, and are you measuring its short-term variation or its long-term variation? Cp and Pp ignore centering; Cpk and Ppk account for it. Cp and Cpk use within-subgroup variation; Pp and Ppk use overall variation.
That is the whole thing: a two-by-two grid. Once you see the grid, the reason a PPAP study reports all four stops being a mystery and starts being obvious. This guide builds the grid one axis at a time, shows exactly how the sigma is estimated differently, and explains why the gap between Cpk and Ppk is one of the most useful numbers you can read. For the underlying bell-curve picture and a worked fill-weight example, the deeper process capability guide draws it out.
What is the difference between Cp, Cpk, Pp, and Ppk?
The four indices differ on two independent axes. The first axis is potential versus actual: the "k" indices (Cpk, Ppk) subtract a penalty for how far off center the process runs, while the non-k indices (Cp, Pp) pretend the process is perfectly centered. The second axis is within versus overall variation: the C indices (Cp, Cpk) use short-term, within-subgroup spread, while the P indices (Pp, Ppk) use the total, long-term spread of all the data. Every one of the four sits at one intersection of those two axes.
What is the real difference between Cp and Pp?
Cp and Pp use identical formulas, spec width divided by six sigma, but they plug in a different sigma, and that difference is the entire point. Cp uses the within-subgroup standard deviation, estimated from the average subgroup range (R-bar divided by d2) or average subgroup standard deviation. That sigma captures only the variation present inside a subgroup, the process at its most stable, over a few consecutive parts. Pp uses the overall standard deviation, the plain sample standard deviation of every individual value in the study, which soaks up drift, tool wear, shift changes, and lot-to-lot wander.
So Cp describes the entitlement of the process: what the spread would be if you removed all the between-subgroup noise. Pp describes what actually happened across the whole study window. In a perfectly stable process the two sigmas are nearly equal and Cp is close to Pp. When they diverge, the process is not stable, something is moving the mean around between subgroups, and that instability is exactly what a control chart exists to catch.
| Index | Formula (two-sided) | Sigma used | Reads centering? |
|---|---|---|---|
| Cp | (USL − LSL) / 6σwithin | within-subgroup (R-bar/d2) | No |
| Cpk | min[(USL − μ), (μ − LSL)] / 3σwithin | within-subgroup | Yes |
| Pp | (USL − LSL) / 6σoverall | overall (sample std dev) | No |
| Ppk | min[(USL − μ), (μ − LSL)] / 3σoverall | overall | Yes |
Why do you read the gaps between the indices?
Each index alone is a grade. The gaps between them are a diagnosis, and they tell you which problem to fix and roughly what it will cost.
- Cp minus Cpk (a within-subgroup pair) measures centering. If Cp is 1.8 but Cpk is 1.1, the spread is fine, the process is just running off-center. That is usually a cheap fix: adjust the setpoint.
- Cpk minus Ppk (same "k", different sigma) measures stability. A healthy Cpk with a much lower Ppk means the process is capable in short bursts but drifts across the study. The within-subgroup math looks great; the customer got the overall reality. Chase the drift, not the spread.
- Pp minus Ppk tells the centering story again, but on the honest long-term sigma, so it is the version that best predicts field fallout.
The most dangerous pattern is a proud Cpk sitting on top of a quietly failing Ppk. It says the process can hit the target when nothing disturbs it, and something is disturbing it constantly. Reporting only Cpk hides that; reporting the pair exposes it.
What is a good value for each index?
The same thresholds apply across all four, because they share the same three-sigma-margin logic. An index of 1.33 means the nearest spec limit sits four standard deviations from the mean, which under normality predicts roughly 30 defective parts per million on that side; 1.67 corresponds to a five-sigma margin (about 0.3 ppm), and 2.0 is the six-sigma margin. By common convention 1.33 is the floor for ongoing production on characteristics that matter, and 1.67 is a frequent bar for initial studies. What changes between indices is not the target, it is which reality the number describes: a 1.67 Cp with a 1.10 Ppk is not a capable process, it is a wide-open process that happens to be centered on a good day.
Read the numbers as a set, in order. First check Cp or Pp: if the spread itself does not fit, no amount of centering will save you, and you are looking at variation reduction, which is expensive. If the spread fits but Cpk lags, re-center, which is usually cheap. If Cpk looks fine but Ppk trails it, stop trusting the short-term number and go hunt the drift. Three different verdicts, three different budgets, and you can only tell them apart by reporting all four.
Why does a PPAP capability study report all four?
Because a customer approving a new part wants both the entitlement and the reality, and wants to see whether the process is stable enough to trust. The four indices together tell a complete story that no single number can: Cp/Pp show whether the spread even fits, Cpk/Ppk show whether it fits as it actually runs, and the C-versus-P comparison shows whether the process held still during the study. That is why the Production Part Approval Process asks for a capability study on identified special characteristics as one of its submission elements.
Automotive practice draws a specific line between the two families. Initial submissions, run over a short window on limited volume, are commonly judged on Ppk because you cannot yet claim the process is stable long-term, so the honest, drift-inclusive number is the fair test. Once the process is validated and running in ongoing production, monitoring shifts toward Cpk paired with SPC where the within-subgroup number tracks the entitlement you are trying to hold. New launches in automotive and aerospace routinely ask for a higher bar on the initial study than on ongoing production.
The reporting convention behind the four indices
The AIAG Production Part Approval Process names process capability and performance results on customer-designated special characteristics as a required submission element, and its default acceptance criteria for initial studies commonly treat an index of 1.67 or higher as acceptable, 1.33 to 1.67 as acceptable pending review, and below 1.33 as not meeting criteria. Initial PPAP studies are typically evaluated on Ppk (overall variation), while ongoing production is monitored on Cpk with SPC.
Sources: AIAG, Automotive Core Tools (PPAP & SPC) · ASQ, Process Capability
How should you compute and report all four?
The math is easy; the sequence and the assumptions are where studies go wrong. Do it in this order.
- Qualify the gauge first. Run a measurement system analysis. If the gauge R&R is poor, the indices measure your gauge, not your process, and the whole study is fiction.
- Collect in rational subgroups. Sample small consecutive groups (commonly 3-5 parts) at set intervals, so within-subgroup captures only short-term noise and between-subgroup captures the drift. Common practice is at least 100 individual values across 20-25 subgroups.
- Plot the control chart and confirm stability. The C indices only mean something on a stable process. Out-of-control points mean there is no single "within" spread to estimate.
- Compute both sigmas. σwithin from R-bar/d2 (or pooled subgroup standard deviation); σoverall as the plain sample standard deviation of all individual values.
- Calculate all four indices and check normality. The parts-per-million predictions assume roughly normal data; skewed characteristics (flatness, runout, anything bounded at zero) need a transformation first.
- Report the set and read the gaps. Present Cp, Cpk, Pp, Ppk together. A big Cp-to-Cpk gap says re-center; a big Cpk-to-Ppk gap says stabilize.
Where capability studies quietly rot
The classic failure is not a bad calculation, it is a study frozen at launch. The four indices get computed once, filed in a PPAP binder, and quoted for years while the tool wears and the mean wanders. Six months later the real Ppk is nowhere near the certificate, and nobody knows because nobody recomputed it. Capability is a snapshot, not a property of the machine, and the same drift that separates Cpk from Ppk in the study keeps working after the study is filed.
The fix is to stop treating capability as an annual archaeology project. When check data is captured digitally at the station instead of on clipboards, a fresh Ppk is always one query away, sitting next to the reject reasons and the downtime log, and the Cpk-to-Ppk gap becomes a live warning rather than a once-a-year surprise. That continuous view of quality data, on top of your existing process with no rip-and-replace, is what Harmony's quality intelligence platform is built to provide. Capability is also where the FMEA and control plan meet the numbers, which is why the characteristics you track here trace straight back through the control plan and FMEA and why the measurement discipline behind them is the same measurement system analysis work that qualifies every gauge. Even a small batch production run deserves the honest Ppk, because one drifting lot is easier to catch on a live number than in a year-old binder.