Cpk and Ppk use the same formula, the distance from the process mean to the nearest specification limit divided by three standard deviations. The only difference is which standard deviation goes in. Cpk uses within-subgroup variation (short-term, usually R̄/d₂), so it shows what the process could do if it stayed centered and stable. Ppk uses the overall standard deviation of every reading, so it shows what the process actually delivered over the study. If Ppk is well below Cpk, something shifts the process between subgroups.
| Cpk (process capability) | Ppk (process performance) | |
|---|---|---|
| Standard deviation used | Within-subgroup sigma, estimated from R̄/d₂ or s̄/c₄ | Overall sample standard deviation of all readings |
| Variation it captures | Short-term, part-to-part variation inside a subgroup | Everything: within-subgroup plus shifts and drift between subgroups |
| Question it answers | What can this process do when it is stable? | What did this process actually produce? |
| Requires statistical control? | Yes. Without control the sigma estimate means little | No, but an unstable process makes the number hard to predict from |
| Data needed | Rational subgroups in time order (for example 25 subgroups of 5) | All individual readings from the study period |
| Typical use | Ongoing monitoring once a process is in control | Initial process studies, PPAP submissions, new or changed processes |
| Usual relationship | Equal to or higher than Ppk | Equal to or lower than Cpk |
Both indexes look at the nearer specification limit, because that is the side where parts will fall out first. With USL and LSL as the upper and lower limits and x̄ as the process mean:
Cpk = min(USL − x̄, x̄ − LSL) ÷ (3 × σ within). Ppk = min(USL − x̄, x̄ − LSL) ÷ (3 × σ overall). The centered versions, Cp and Pp, ignore the mean and divide the full tolerance (USL − LSL) by six sigma. They tell you how well the spread fits the tolerance if the process were perfectly centered.
σ within is usually estimated from a range chart as R̄ ÷ d₂, where d₂ depends on subgroup size (2.326 for subgroups of 5). σ overall is the ordinary sample standard deviation, the STDEV.S function in Excel, run across every reading. You can run either calculation in the process capability calculator.
Within-subgroup sigma only sees variation between consecutive parts, typically made minutes apart. Anything that moves the process between subgroups, such as tool wear, a new material lot, a different operator, a temperature swing, or a setup change, never shows up in R̄. It does show up in the overall standard deviation.
So a gap between Cpk and Ppk is a diagnostic. When the two are close, the process is behaving the same way all the time and Cpk is a fair prediction of the future. When Ppk is much lower, the process has a special cause you have not removed yet. Look at the X̄ chart: shifts, trends and out-of-control points explain the gap. The statistical process control guide covers how to read those charts.
Automotive customers following the AIAG PPAP manual ask for Ppk in the initial process study, because a new process has no control history yet. The manual treats an index above 1.67 as meeting acceptance, 1.33 to 1.67 as possibly acceptable with customer agreement, and below 1.33 as not acceptable. Many customers set their own numbers in customer-specific requirements, and those override the manual, so read your customer’s supplier manual first. The PPAP guide and PPAP checklist show where the study fits in the submission.
Once the process is in production and in control, Cpk is the usual number on the control plan for special characteristics, with 1.33 a common minimum. Report both when you can. A pair of numbers tells a reviewer far more than either one alone.
Capability math assumes the measurements are good, the data are roughly normal, and there are enough of them. Check the gauge first: if measurement variation eats a large share of the tolerance, both indexes are understated. Run a gage R&R study before the capability study, not after. How to run a gauge R&R study covers the setup.
The AIAG SPC manual suggests 25 or more subgroups and about 100 or more individual readings for a capability study. With 30 readings, the confidence interval on Cpk is wide enough that 1.33 and 1.0 can be statistically indistinguishable. For strongly skewed characteristics such as flatness, runout or surface finish, use a non-normal method or a transformation rather than the normal-theory formula.
If a reviewer asks how many defects to expect, convert the index to a defect rate with the DPMO and sigma calculator, remembering that the conversion only holds for a stable, normal process.
Example: A shaft diameter with a hidden shift (fictional data). Specification 10.00 ± 0.05 mm, so LSL = 9.95 and USL = 10.05. 25 subgroups of 5 parts, mean x̄ = 10.008 mm, average range R̄ = 0.021 mm, overall standard deviation s = 0.0125 mm.
Result: Cpk 1.55 looks healthy, but Ppk 1.12 is below the 1.33 that PPAP initial studies treat as the floor. Overall sigma is about 38% larger than within sigma, so the X̄ chart will show shifts between subgroups. Find and remove that cause before submitting.
Example: The same shaft after the cause is fixed (fictional data). The mean is now centered at 10.000 mm, σ within = 0.0100 mm and overall s = 0.0104 mm.
Result: Cpk and Ppk are now within 0.07 of each other. The process behaves the same within and between subgroups, so Cpk is a fair prediction of future output.
Occasionally, by a small amount, because both sigmas are estimates. A Ppk well above Cpk usually means the subgroups were not rational, for example parts from different cavities or spindles mixed in one subgroup, which inflates R̄.
In practice it is used that way, but it is better to say Ppk describes the study period. It is only a long-term figure if the study covered the sources of long-term variation, such as several material lots, shifts and setups.
1.33 is a common minimum for ongoing production and 1.67 is a common target for safety or critical characteristics. Your customer’s requirements decide, so check their supplier manual.
Not to do the arithmetic. You still should chart the data, because a Ppk from an unstable process describes the past and says little about what the next lot will do.
Use only the side that exists. For a maximum-only limit, Cpk = (USL − x̄) ÷ 3σ within and Ppk = (USL − x̄) ÷ 3σ overall. Cp and Pp are not defined.
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