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Cpk vs Ppk: what's the difference?

Short answer: both compare your process to the specification limits, and both take centering into account. The difference is which standard deviation they use.

Cpk uses the within-subgroup (short-term) standard deviation, usually estimated as R̄/d₂. It shows what the process could do if the variation between subgroups (shifts, drift, setups) were removed.
Ppk uses the overall (long-term) standard deviation of all the data. It shows what the process actually delivered, including shifts and drift.

If the process is stable (in statistical control), the two numbers are close. A big gap, with Cpk much higher than Ppk, tells you the process moves around between subgroups, and you can gain a lot by finding out why.

The formulas

	Uses σ from	Formula
Cp	within subgroups	(USL − LSL) / 6σ_within
Cpk	within subgroups	min(USL − x̄, x̄ − LSL) / 3σ_within
Pp	overall	(USL − LSL) / 6σ_overall
Ppk	overall	min(USL − x̄, x̄ − LSL) / 3σ_overall

Worked example

A shaft diameter has LSL = 9.4 mm and USL = 10.6 mm. You collect 25 subgroups of 5 parts. The grand mean is x̄ = 10.1 mm and the average range is R̄ = 0.2326 mm. The standard deviation of all 125 readings is s = 0.15 mm.

σ within = R̄ / d₂ = 0.2326 / 2.326 = 0.100 (d₂ = 2.326 for n = 5) σ overall = s = 0.150 Nearest spec limit: USL (10.6 − 10.1 = 0.5; the LSL side is 10.1 − 9.4 = 0.7) Cpk = 0.5 / (3 × 0.100) = 1.67 Ppk = 0.5 / (3 × 0.150) = 1.11 Cp = 1.2 / (6 × 0.100) = 2.00 Pp = 1.2 / (6 × 0.150) = 1.33

What it means: in the short term this process is very capable (Cpk 1.67). Over the whole run it delivered only Ppk 1.11, because the mean or spread moved between subgroups. Check the control chart for shifts, look at setups and material lots, and re-center: the process sits 0.1 mm above the middle of the tolerance.

Want to try your own numbers? The free process capability calculator opens with this example loaded and adds CPU/CPL, the centering factor k, expected PPM on each side and a curve.

Common exam traps

Swapping the σ's. Cpk uses the within-subgroup σ (R̄/d₂ or s̄/c₄), and Ppk uses the overall sample standard deviation.
Using the farther spec limit. Cpk and Ppk always use the limit nearer to the mean, which gives the smaller of the two one-sided values.
Dividing by 6σ instead of 3σ. The one-sided indices (Cpk, Ppk) divide by 3σ, and Cp and Pp divide by 6σ.
Thinking Cpk can be bigger than Cp. It can't. Cpk equals Cp only when the process is perfectly centered.
Reporting capability for an unstable process. Capability indices only predict future output when the process is in control. If the chart shows special causes, fix those first.

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