The one-line difference
Cpk and Ppk are both (distance from mean to nearest limit) / 3σ. The only difference is which σ you use. Cpk uses σ within: the spread inside short subgroups, usually estimated as R̄/d₂ or s̄/c₄ from an X̄-R or X̄-s chart. Ppk uses σ overall: the ordinary sample standard deviation of every value in the study.
If the process mean wanders between subgroups (tool wear, shift change, a new material batch, a warm-up after lunch), σ overall grows and σ within does not. So the gap between Cpk and Ppk is a measure of how much the process moves over time. That gap is often more useful than either number on its own.
Worked example: shaft diameter
A turned shaft has a diameter specification of 10.00 ± 0.30 mm, so LSL = 9.70 and USL = 10.30. The supplier runs 25 subgroups of 5 parts. The data (fictional) gives:
- Mean of all 125 values: 10.05 mm
- σ within (R̄/d₂): 0.05 mm
- σ overall (sample standard deviation): 0.07 mm
| Index | Calculation | Result |
|---|---|---|
| Cp | 0.60 / (6 × 0.05) | 2.00 |
| Cpk | min(0.25 / 0.15, 0.35 / 0.15) = min(1.67, 2.33) | 1.67 |
| Pp | 0.60 / (6 × 0.07) | 1.43 |
| Ppk | min(0.25 / 0.21, 0.35 / 0.21) = min(1.19, 1.67) | 1.19 |
On Cpk alone this process meets a 1.67 requirement. On Ppk it misses even 1.33. Under a normal model, the expected out-of-spec rate is about 0.3 ppm with σ within, but about 178 ppm with σ overall, almost all of it above the USL. The parts the customer receives come from the overall distribution, not from one subgroup.
Two separate problems hide in this example. First, the mean sits 0.05 mm above nominal. Centering the process at 10.00 with the same σ overall would give Ppk = 0.30 / 0.21 = 1.43 and about 18 ppm. Second, σ overall is 1.4 times σ within, so something shifts between subgroups. Find that cause before you tune the offset; otherwise the next shift undoes it.
Check the numbers yourself in the Cpk / Ppk calculator: enter USL 10.30, LSL 9.70, mean 10.05, then σ 0.05 and σ 0.07.
Reading the gap
- Cpk ≈ Ppk: the process is close to stable. The number you report is believable, as long as the sample is big enough.
- Cpk clearly above Ppk: special causes between subgroups. Look at the X̄ chart for trends, steps and out-of-control points.
- Cp clearly above Cpk: the spread is fine but the mean is off-center. Usually a setting or offset problem.
- Ppk above Cpk: usually estimation noise or a calculation error (wrong subgroup size constant, mixed streams); also check negative autocorrelation or over-adjustment between parts.
Checks before you send a capability study
- Is the process stable on a control chart? A Cpk from an unstable process predicts nothing.
- Is the gauge good enough? Run the MSA first; gauge spread counts as process spread.
- Is the data roughly normal? If it is skewed (flatness, runout, roughness often are), use a non-normal method and say so.
- Are the subgroups rational: consecutive parts from one machine, one cavity, one spindle?
- Does the study say which σ it used, how many values, and the date range?
- Does it meet the index the customer actually asked for (Ppk vs Cpk, 1.33 vs 1.67)?
Where this shows up in an 8D
When a dimensional complaint lands, the old PPAP Cpk is often waved around as proof the process is capable. Ask which σ it used and when it was run. A Ppk on recent production says more about what escaped. After the fix, a new study on the same characteristic is good D6 verification evidence, and the control plan should be updated to match (see PFMEA and control plan update after an 8D). To turn the index into an expected defect rate, see PPM vs Cpk.
FAQ
- What is the difference between Cpk and Ppk?
- Both use the same formula: the distance from the mean to the nearest specification limit, divided by three sigma. Cpk uses sigma within subgroups (short-term, for example R-bar/d2 from a control chart). Ppk uses the overall standard deviation of all values (long-term). Ppk includes shifts between subgroups; Cpk does not.
- Which one does the customer want in a PPAP?
- Read the customer's supplier manual first. Many automotive customers ask for Ppk in the initial process study, because the run is short and stability is not yet proven, and for Cpk once the process is in ongoing production under SPC. A common requirement is 1.67 for the initial study and 1.33 ongoing. A result between 1.33 and 1.67 is often treated as conditional or needs customer agreement in an initial study. The customer's document decides.
- Can Ppk be higher than Cpk?
- Rarely, and only by a small margin: usually estimation noise or a calculation error (also check negative autocorrelation or over-adjustment between parts). If Ppk is clearly above Cpk, check how sigma within was calculated (wrong d2 constant, subgroups mixed across machines) before you report either number.
- How many parts do I need for a capability study?
- A common rule is at least 25 subgroups (about 100 values) for Cpk, or at least 30 individual values as a bare minimum. With fewer values the estimate moves a lot from sample to sample, so label it preliminary.
- Does a good Cpk mean the 8D corrective action worked?
- Only if the study was run on the characteristic that failed, after the change, on a stable process, with enough data. Capability is one piece of D6 evidence, not the whole D6.