What Cpk measures
Cpk tells you how far the nearest specification limit is from the process mean, measured in units of three standard deviations. It reflects both how much the process varies and whether it is centered between its limits. A supplier reporting a Cpk of 1.33 on a dimension is saying the process mean sits four standard deviations inside the closer limit.
Cpk only means something for a stable process, a characteristic measured on a continuous scale and a measurement system you can trust. Outside those conditions, a Cpk figure looks precise and says very little.
The formulas
Cp = (USL - LSL) / (6 × σ)
Cpk = min[ (USL - μ) / (3 × σ) , (μ - LSL) / (3 × σ) ]- USL, LSL: upper and lower specification limits
- μ: process mean
- σ: process standard deviation
Cp compares the width of the tolerance with the spread of the process, ignoring where the process sits. Cpk uses the closer limit, so it falls when the process drifts off center. Cp and Cpk are equal only when the process is exactly centered. For a one-sided specification, such as a minimum pull-out force, use only the side that exists.
Cpk and Ppk
The two use the same formula with different estimates of σ. Cpk uses short-term, within-subgroup variation, usually estimated from control chart subgroups. Ppk uses the overall standard deviation of all the data, including shifts between subgroups over time. If Ppk is much lower than Cpk, the process moves between subgroups: from shift to shift, lot to lot or cavity to cavity.
Reading the numbers
For a stable, normally distributed process:
| Cpk | Distance from mean to nearest limit | Approx. out of spec beyond that limit |
|---|---|---|
| 1.00 | 3σ | about 1,350 parts per million |
| 1.33 | 4σ | about 32 parts per million |
| 1.67 | 5σ | under 1 part per million |
| 2.00 | 6σ | about 0.001 parts per million |
If the process is centered, the far limit adds about the same again. 1.33 is a widely used minimum for ongoing production. Automotive part approval (AIAG PPAP) generally treats a preliminary capability index, usually Ppk, above 1.67 as acceptable for a new process; customers’ own requirements take precedence. Many hardware programs ask for 1.33 on critical characteristics and accept lower values elsewhere with added inspection.
Conditions for a meaningful Cpk
- A stable process. Check a control chart first. The capability of an unstable process predicts nothing.
- Enough data. A common rule of thumb is at least 100 measurements collected over time in rational subgroups, for example 25 subgroups of four or five parts. Five parts measured once give a very uncertain estimate.
- A trusted measurement system. A gauge study (GR&R) should show that measurement variation is small relative to the tolerance.
- Separate streams. For a multi-cavity mold or several lines, calculate per cavity or per line. Mixing them hides a bad stream.
- Unfiltered data. Include every measured part, out-of-spec ones too. Data that has already been sorted cuts off the tails and inflates Cpk.
How Cpk is used with OEM/ODM partners
Buyers usually ask for Cpk on critical-to-quality characteristics: dimensions that control fit or sealing, key electrical values, torque, force or weight. It typically appears after first article inspection and during pilot builds, again before mass production and periodically after. Asking for Cpk on every dimension of every part creates paperwork without improving quality; choose the characteristics that matter.
Cpk does not apply to pass/fail attributes such as cosmetic defects. For those, use defect rates, first pass yield and lot sampling (AQL).
Questions to ask about a supplier’s Cpk data
- Which characteristic, which limits and which drawing revision?
- How many parts, over what period and in what subgroups?
- Per cavity, line or machine, or combined?
- Was the process in control, and can you share the control chart?
- Was a gauge study done on the measuring method?
- Can you share the raw data, not only the index?
Where Zefinity helps
A supplier can produce a Cpk figure for almost any characteristic; the useful decision is which ones deserve one. Through QA and ongoing supplier performance management, Zefinity helps teams choose which characteristics to monitor, agree how suppliers collect and report the data, and follow up through corrective action when capability drops.
Frequently asked questions
What is a good Cpk value?
1.33 is a widely used minimum for ongoing production, and 1.67 or higher is common for new processes or safety-related characteristics. Below 1.0, a process makes out-of-spec parts even when it is centered and stable. The right target depends on how critical the characteristic is and what later inspection would catch.
What is the difference between Cp and Cpk?
Cp compares the tolerance width with the process spread and ignores where the process is centered. Cpk uses the distance from the mean to the nearer limit, so it drops when the process drifts off center. A process can have a high Cp and a low Cpk if it is capable but badly centered.
Can Cpk be calculated from a few samples?
It can be calculated, but it will not mean much. With only a handful of parts, the uncertainty in the estimated standard deviation is so large that the true index could be far higher or lower. Use a larger set of measurements, commonly around 100 or more, collected over time from a stable process.