Cpk vs Ppk: what is the difference?
Cpk and Ppk use the same formula with a different sigma. Learn when each one applies, why they differ and what a gap between them tells you, with a worked example.
Updated 2026-10-24
Same formula, different sigma
Both indices compare the distance from the process mean to the nearest specification limit with three standard deviations:
Cpk = min(USL − μ, μ − LSL) / (3 · σ_within)Ppk = min(USL − μ, μ − LSL) / (3 · σ_overall)
The only difference is the standard deviation. σ within is estimated from the variation inside rational subgroups, usually consecutive parts: R̄ / d₂, S̄ / c₄ or MR̄ / 1.128. It describes the short-term noise of the process. σ overall is the ordinary standard deviation of all values. It contains everything: short-term noise plus shifts and drift between subgroups.
What the gap tells you
For a perfectly stable process both sigmas estimate the same thing and Cpk ≈ Ppk. When the process moves between subgroups, σ overall becomes larger and Ppk falls below Cpk. Cpk then says what the process could do if it stayed where it was, Ppk says what the customer actually received.
| Situation | What to do |
|---|---|
| Cpk ≈ Ppk, both high | Capable and stable. Keep monitoring. |
| Cpk high, Ppk low | The process drifts or shifts. Look for tool wear, warm-up, material batches, operator changes. A control chart will show where. |
| Both low, Cp high | The spread is fine but the process is off centre. Move the mean to the target. |
| Both low, Cp low | The variation itself is too large. Reduce it, or review the tolerance with design. |
Worked example
A shaft diameter has a specification of 25.000 ± 0.100 mm. 25 subgroups of 5 parts give a mean of 25.020, σ within 0.010 and σ overall 0.016.
- Cpk = (25.100 − 25.020) / (3 × 0.010) = 2.67
- Ppk = (25.100 − 25.020) / (3 × 0.016) = 1.67
Short term the process is excellent, but the large gap shows that the mean moves between subgroups. The X-bar chart will show the drift, and fixing it (for example automatic tool compensation) brings Ppk up towards Cpk.
Paste your own data into the process capability calculator: it shows both indices side by side, with the control charts that explain the difference.
Which one does my customer want?
The AIAG PPAP manual asks for Ppk in the initial process study (or Cpk once stability is proven), see PPAP capability requirements. Many customers ask for both. Report both, and always together with the control chart: an index from an unstable process does not predict anything.