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Cpk vs Ppk: the only real difference is which standard deviation you use

Same mean, same specification limits, different sigma. Here is what that gap is telling you about your process.

Updated 13 November 2026 · 7 min read · Written for working labs and quality teams

The two formulas side by side

Both indices compare the distance from the process mean to the nearest specification limit against three sigmas. The only thing that changes is the sigma:

Practical note. Cp and Pp ignore centering entirely — a process sitting right on the upper limit can still show a beautiful Cp. Always read the index together with the mean and the histogram, never as a standalone pass mark.

A worked example with real numbers

A turned shaft is specified at 10.00 ± 0.20 mm, so LSL = 9.80 and USL = 10.20. You collect 25 subgroups of 5. The grand mean μ = 10.02, the within-subgroup sigma from R̄/d2 is 0.030, and the overall standard deviation of all 125 values is 0.055.

Cpk = min[(10.20 − 10.02) / (3 × 0.030), (10.02 − 9.80) / (3 × 0.030)] = min[2.00, 2.44] = 2.00.

Ppk = min[(10.20 − 10.02) / (3 × 0.055), (10.02 − 9.80) / (3 × 0.055)] = min[1.09, 1.33] = 1.09.

Nothing is wrong with the arithmetic. The process is capable in the short term (2.00) but the overall performance is only 1.09, because subgroup means wandered — tool wear, a shift change, a warm-up drift, or two batches of material. Reporting only the 2.00 would be the mistake.

When to report which one

• Initial submission / PPAP: customers commonly ask for Ppk ≥ 1.67 from the initial run, because it reflects everything that actually happened. This is a customer or AIAG PPAP convention, not an ISO 9001 or IATF 16949 clause requirement.
• Series production monitoring: Cpk ≥ 1.33 is the most common contractual target, again a customer requirement rather than a line in the standard.
• Both together: the gap itself is the diagnostic. If Cpk ≈ Ppk, common-cause variation dominates and the process is behaving predictably. If Cpk is much larger, hunt for special causes between subgroups before quoting any capability number.
• Neither: if the process is not stable, or the data are strongly non-normal, a capability index is a number without a model behind it. Stabilise first, or use a transformation / non-normal method and say which one you used.

Four checks before you calculate anything

1. Measurement system first. If the gage R&R is poor relative to the tolerance, the spread you are measuring belongs partly to the gage, not the process.
2. Rational subgroups. Put parts made under the same conditions in one subgroup; otherwise within-subgroup sigma is contaminated by exactly the drift you are trying to detect.
3. Enough data. A Cpk from 8 values is a point estimate with a very wide confidence interval. The commonly used floor is roughly 25 subgroups / 100 values, and the estimate should be reported with its uncertainty if a decision hinges on it.
4. Right chart, right limits. Control limits come from process data; specification limits come from the customer. Drawing a spec line on an X̄ chart as if it were a control limit is the single most common shop-floor error.

Where this goes wrong in practice

Computing Cpk with the overall sample standard deviation. You get Ppk twice and lose the only signal that separates short-term capability from long-term drift.

Quoting Cpk on an unstable process. An index assumes a stable, predictable distribution; an out-of-control chart invalidates the premise, not just the number.

Treating 1.33 as law. It is a widespread customer target. Check the contract, the control plan and the customer-specific requirements before you set an acceptance threshold.

Averaging Cpk values across shifts or cavities instead of looking at each stream separately — two healthy streams straddling the mean can hide a bimodal mess.

Frequently asked

Is Cpk always higher than Ppk?
Usually, because overall variation includes within-subgroup variation plus any between-subgroup movement. But it is not a mathematical guarantee: with unusual subgroup patterns the overall estimate can be smaller than the within estimate. Treat the gap as a diagnostic, not a rule.

What is a good Cpk value?
It depends on the contract and the risk. 1.33 is the most common series-production target and 1.67 is often requested for initial or safety-related characteristics; neither appears as a number in ISO 9001 or IATF 16949. For safety or regulated characteristics, the customer-specific requirements govern.

Can Cpk be negative?
Yes. If the process mean has moved outside a specification limit, the distance to that limit is negative, so the minimum becomes negative. It means the process is producing out-of-spec material at the centre of its distribution, not merely in a tail.

Do I need both Cpk and Ppk for a submission?
Most automotive customers ask for the initial-process performance index (Ppk) from the submission run and capability (Cpk) once the process is stable. Check the submission level and customer-specific requirements — the required index and minimum are contractual, not universal.

LabKitPro guides are written from published standards and accreditation-body documents — references, clause numbers and paraphrased intent only, never verbatim standard text. They are for preparation and study, not a certification or accreditation decision, and not legal advice. ISO standards are trademarks of ISO; IATF 16949 is published by the International Automotive Task Force and is not an ISO standard. The current laboratory standard is ISO/IEC 17025:2017; there is no 2025 edition. Global ACI replaced IAF and ILAC on 1 January 2026.

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