Cp Cpk Pp and Ppk - What Each Index Actually Tells You

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Aug 22nd, 2026

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Four capability indices, two letters different, and engineers still report the wrong one on customer PPAP submissions. Cp, Cpk, Pp, and Ppk aren't four ways of saying the same thing with slightly different math — they answer two genuinely different questions, and mixing them up misrepresents what the process is actually doing.
## The First Split: Within vs. Overall Sigma
Cp and Cpk are calculated using within-subgroup sigma — the estimate of short-term, common-cause variation derived from the average range or average standard deviation across subgroups (the same R-bar/d2 or S-bar/c4 relationship that drives control chart limits). This captures what the process is capable of when it's running consistently, subgroup to subgroup, with the special causes stripped out.
Pp and Ppk use overall sigma — the standard deviation calculated across every individual data point in the dataset, ignoring subgroup structure entirely. This captures everything: the short-term variation plus any drift, shift, or special-cause variation that occurred across the sampling period.
Cp/Cpk describe potential capability — what the process could achieve if it stayed as consistent as it is within each subgroup. Pp/Ppk describe actual performance over the period sampled, drift included. A process can have a strong Cpk and a weak Ppk simultaneously, and that gap is diagnostic information, not noise: it means the process is capable in the short term but something — tool wear, temperature drift, shift-to-shift variation — is pulling the long-term output around.
Reporting Cpk alone hides that gap. Reporting Ppk alone hides whether the underlying process is fundamentally capable or just poorly controlled. A capability study that only reports one of the two pairs is giving an incomplete picture, and most customer quality requirements (AIAG core tools among them) expect both.
## The Second Split: Centered vs. Off-Center
Within each pair, the second letter changes what's being measured relative to.
Cp compares the spec width to the process spread, full stop — it doesn't care where the process mean sits relative to the tolerance. A process can have an excellent Cp while running dangerously close to one spec limit, because Cp assumes perfect centering that may not exist.
Cpk accounts for centering. It calculates the distance from the process mean to the nearest spec limit, divided by three sigma, and takes the smaller of the two one-sided calculations (upper and lower). A process that's shifted toward one limit will show a Cpk noticeably lower than its Cp — and that gap is the tell. If Cp is comfortable but Cpk isn't, the process has enough inherent spread to work but is running off-center, which is a correctable centering problem rather than a variation-reduction problem.
The same relationship holds between Pp and Ppk.
## Reading the Four Together
The full picture comes from looking at all four side by side, not any one in isolation:
- High Cp, low Cpk: process has the spread to work, but it's off-center. Fix the centering, not the variation.
- Cpk close to Ppk: the process is behaving consistently across the sampling period — no meaningful drift.
- Cpk noticeably higher than Ppk: something is pulling long-term performance away from short-term potential. Look for drift sources — tool wear, environmental effects, operator or shift differences.
- Low Cp and low Pp together: the process doesn't have the inherent capability to meet spec even under ideal, centered conditions. That's a fundamental variation-reduction problem, not a centering fix.
## A Note on Non-Normal Data
All four indices assume the underlying data is normally distributed. Running standard Cp/Cpk/Pp/Ppk math on a distribution that's meaningfully skewed — common with parameters like flatness, roundness, or anything bounded at zero — produces indices that misstate real capability. A normality check should precede the capability calculation, not follow it as an afterthought once the number looks wrong.
## Calculating It Correctly
Getting within-sigma and overall-sigma right — pulling the correct constant for the subgroup size, checking normality before trusting the result, and reporting all four indices together rather than whichever one looks best — is where manual capability studies most often go wrong. [SigmaDesk's process capability calculator](https://sigmadesk.app/process-capability-calculator/) calculates Cp, Cpk, Pp, and Ppk side by side with a built-in normality check, free in the browser. It's part of the broader [SigmaDesk](https://sigmadesk.app/) SPC platform, alongside control charts, Gage R&R, and attribute charts.
Report all four together. The gaps between them are usually more informative than any single number.

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Four capability indices, two letters different, and engineers still report the wrong one on customer PPAP submissions. Cp, Cpk, Pp, and Ppk aren't four ways of saying the same thing with slightly different math — they answer two genuinely different questions, and mixing them up misrepresents what the process is actually doing.

## The First Split: Within vs. Overall Sigma

Cp and Cpk are calculated using within-subgroup sigma — the estimate of short-term, common-cause variation derived from the average range or average standard deviation across subgroups (the same R-bar/d2 or S-bar/c4 relationship that drives control chart limits). This captures what the process is capable of when it's running consistently, subgroup to subgroup, with the special causes stripped out.

Pp and Ppk use overall sigma — the standard deviation calculated across every individual data point in the dataset, ignoring subgroup structure entirely. This captures everything: the short-term variation plus any drift, shift, or special-cause variation that occurred across the sampling period.

Cp/Cpk describe potential capability — what the process could achieve if it stayed as consistent as it is within each subgroup. Pp/Ppk describe actual performance over the period sampled, drift included. A process can have a strong Cpk and a weak Ppk simultaneously, and that gap is diagnostic information, not noise: it means the process is capable in the short term but something — tool wear, temperature drift, shift-to-shift variation — is pulling the long-term output around.

Reporting Cpk alone hides that gap. Reporting Ppk alone hides whether the underlying process is fundamentally capable or just poorly controlled. A capability study that only reports one of the two pairs is giving an incomplete picture, and most customer quality requirements (AIAG core tools among them) expect both.

## The Second Split: Centered vs. Off-Center

Within each pair, the second letter changes what's being measured relative to.

Cp compares the spec width to the process spread, full stop — it doesn't care where the process mean sits relative to the tolerance. A process can have an excellent Cp while running dangerously close to one spec limit, because Cp assumes perfect centering that may not exist.

Cpk accounts for centering. It calculates the distance from the process mean to the nearest spec limit, divided by three sigma, and takes the smaller of the two one-sided calculations (upper and lower). A process that's shifted toward one limit will show a Cpk noticeably lower than its Cp — and that gap is the tell. If Cp is comfortable but Cpk isn't, the process has enough inherent spread to work but is running off-center, which is a correctable centering problem rather than a variation-reduction problem.

The same relationship holds between Pp and Ppk.

## Reading the Four Together

The full picture comes from looking at all four side by side, not any one in isolation:

- High Cp, low Cpk: process has the spread to work, but it's off-center. Fix the centering, not the variation.
- Cpk close to Ppk: the process is behaving consistently across the sampling period — no meaningful drift.
- Cpk noticeably higher than Ppk: something is pulling long-term performance away from short-term potential. Look for drift sources — tool wear, environmental effects, operator or shift differences.
- Low Cp and low Pp together: the process doesn't have the inherent capability to meet spec even under ideal, centered conditions. That's a fundamental variation-reduction problem, not a centering fix.

## A Note on Non-Normal Data

All four indices assume the underlying data is normally distributed. Running standard Cp/Cpk/Pp/Ppk math on a distribution that's meaningfully skewed — common with parameters like flatness, roundness, or anything bounded at zero — produces indices that misstate real capability. A normality check should precede the capability calculation, not follow it as an afterthought once the number looks wrong.

## Calculating It Correctly

Getting within-sigma and overall-sigma right — pulling the correct constant for the subgroup size, checking normality before trusting the result, and reporting all four indices together rather than whichever one looks best — is where manual capability studies most often go wrong. [SigmaDesk's process capability calculator](https://sigmadesk.app/process-capability-calculator/) calculates Cp, Cpk, Pp, and Ppk side by side with a built-in normality check, free in the browser. It's part of the broader [SigmaDesk](https://sigmadesk.app/) SPC platform, alongside control charts, Gage R&R, and attribute charts.

Report all four together. The gaps between them are usually more informative than any single number.