What is the difference between Cpk and Ppk?

Cpk uses the within-subgroup standard deviation (R̄/d₂), so it estimates what the process could do if only common-cause variation remained. Ppk uses the overall sample standard deviation and captures drift and shift between subgroups too. Ppk is usually the smaller and the more honest of the two.

Yes. A negative Cpk means the process mean has moved outside a specification limit, so the majority of output is non-conforming.

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Cp and Cpk Process Capability Calculator

Capability indices compare the voice of the process (its spread) to the voice of the customer (the specification limits). Cp asks whether the process is tight enough to fit. Cpk asks whether it is tight enough and centred. A process can have excellent Cp and terrible Cpk simply by sitting off-target.

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Formula

Potential capabilityCp = (USL − LSL) / (6σ)

Upper capabilityCpu = (USL − μ) / (3σ)

Lower capabilityCpl = (μ − LSL) / (3σ)

Actual capabilityCpk = min(Cpu, Cpl)

Performance indexPpk uses the overall standard deviation s, Cpk uses the within-subgroup estimate σ̂ = R̄ / d₂

Worked example

A machined bore has USL = 10.5 mm, LSL = 9.5 mm. The process runs at μ = 10.1 mm with σ = 0.12 mm.

Cp = (10.5 − 9.5) / (6 × 0.12) = 1.0 / 0.72 = 1.389
Cpu = (10.5 − 10.1) / (3 × 0.12) = 0.4 / 0.36 = 1.111
Cpl = (10.1 − 9.5) / (3 × 0.12) = 0.6 / 0.36 = 1.667
Cpk = min(1.111, 1.667) = 1.111

Cp of 1.39 says the spread would comfortably fit the tolerance. Cpk of 1.11 says it currently does not, because the mean sits 0.1 mm above centre. Re-centring the process to 10.0 mm would raise Cpk to 1.389 with no reduction in variation at all — the cheapest capability improvement available.

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How to interpret the result

Cpk < 1.00	Process is producing out-of-specification parts. Containment required.
Cpk = 1.33	Common minimum for ongoing production (4σ between mean and nearest limit).
Cpk = 1.67	Typical requirement for safety-critical or new-process qualification.
Cpk = 2.00	Six Sigma capability, roughly 2 defective parts per billion under a centred normal model.

Common mistakes

Computing Cpk on data that is not normal or not in control. Both assumptions must hold or the index is meaningless — check the control chart before the capability study.
Confusing Cpk with Ppk. Cpk uses within-subgroup variation and describes potential; Ppk uses total variation and describes what the customer actually received.
Calculating Cp for a one-sided specification. With only one limit, only Cpu or Cpl exists.
Running a capability study on fewer than about 30 measurements, or on parts from a single setup.

Frequently asked questions

What is the difference between Cpk and Ppk?: Cpk uses the within-subgroup standard deviation (R̄/d₂), so it estimates what the process could do if only common-cause variation remained. Ppk uses the overall sample standard deviation and captures drift and shift between subgroups too. Ppk is usually the smaller and the more honest of the two.
Can Cpk be negative?: Yes. A negative Cpk means the process mean has moved outside a specification limit, so the majority of output is non-conforming.

About Reliability Pro

Process Capability is part of a suite of 126 reliability, maintenance and quality engineering tools covering life data analysis, accelerated testing, system reliability, FMEA and root cause, SPC, and design for reliability. It runs in the browser and as native iOS and Android apps, so the same calculation is available at a desk or in front of the asset.

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