Engineering Answers / Production & Quality
Cpk 1.33 is quoted in almost every quality agreement and understood in very few. It is a statement about a process, measured by a system, that has to be in control before the number means anything.
Cpk 1.33 means the distance from the process mean to the nearest specification limit is 4 standard deviations, which corresponds to roughly 63 parts per million outside the limits if the process stays centred. On a molded silicone part, that number is only honest if the measurement system contributes less than about 30% of the observed variation, the process is in statistical control, and at least 125 data points were used. A calliper on a 40 Shore A wall fails the first condition, and the resulting Cpk describes the inspector, not the process.
Cpk is the distance from the process mean to the nearest specification limit, divided by three standard deviations.
At Cpk 1.33, that distance is 4σ. For a centred, normally distributed process, the expected fallout is about 63 parts per million. At 1.00 it is about 2,700 ppm; at 1.67, under 1 ppm.
| Cpk | Distance to limit | Expected fallout | Commercial meaning |
|---|---|---|---|
| 1.00 | 3σ | ~2,700 ppm | Marginal; any drift puts parts out |
| 1.33 | 4σ | ~63 ppm | The conventional floor |
| 1.67 | 5σ | under 1 ppm | Safety-critical characteristics |
| 2.00 | 6σ | effectively zero | Expensive to prove, rarely justified |
1. The process has to be in control. Cpk assumes a stable process. If the mean is drifting — a tool warming through the shift, a compound lot change, ambient humidity rising in the afternoon — the data are not from one distribution and the index is a fiction. Plot the data before calculating anything. A run chart that wanders invalidates the Cpk no matter how good the arithmetic looks.
2. There have to be enough data. Twenty-five subgroups of five is the conventional minimum, and it is not arbitrary: with fewer points the estimate of σ is itself too uncertain to support a claim about 63 ppm. A capability study on ten parts measures the ten parts.
3. The measurement system has to be adequate. Gage R&R should account for less than about 30% of the observed variation, and less than 10% is good. If the measurement system eats half the tolerance, the Cpk is a description of the inspector's technique.
On a machined metal part, the measurement system is usually the least of the problems. On a molded silicone part it is often the dominant one, for reasons that are physical:
The fix is procedural: define the method (non-contact, low-force, or potted cross-section), define the relaxation time, run Gage R&R before the capability study, and keep the instrument with the part record.
A customer specified ±0.10 mm on the wall of a 45 Shore A sealing section and required Cpk 1.33. The first study came back at 0.9. Before touching the process we ran Gage R&R: the calliper method accounted for 61% of the variation. Switching to a low-force gauge brought it to 24%, and Cpk rose to 1.31 without a single change to the tool. The remaining gap was real, and it was closed by widening the tolerance to ±0.15 mm, which the function allowed. The process was never the problem — the measurement and the drawing were.
A report missing the Gage R&R and the run chart is a number without a foundation. It may well be right, but there is no way to tell, and on a soft part the odds are that it is describing the gauge.
If the measurement system is sound and the process is in control and the capability still will not reach 1.33, the tolerance is wrong for the process. Two honest options:
What does not work is asking the press to hold a tolerance the material cannot hold. On silicone that request produces a scrap rate, a lot of process tweaking, and a capability report that is quietly calculated on the best cavity.
Because 1.0 leaves no room for drift. A process at Cpk 1.00 sits exactly three standard deviations from the nearest limit, so a small shift in the mean puts parts outside immediately. Cpk 1.33 gives a buffer of one standard deviation against normal process drift, and it has become the conventional floor in automotive and medical supply chains for that reason. It is a convention, not a law of nature — some characteristics genuinely only need 1.0, and some safety-critical ones are specified at 1.67.
Cpk uses the within-subgroup variation and assumes the process is stable; Ppk uses the overall variation including drift between subgroups. If a process wanders — a tool warming up, a compound lot change, an ambient humidity shift — Ppk is lower than Cpk and is the more honest number for what the customer will receive. A report that shows only Cpk on a process that has not been shown to be in control is a favourable estimate, not a capability.
First check the measurement system, because that is the usual cause on soft parts. If Gage R&R is under 30% and the process is still not capable, the tolerance is tighter than the process can support and the drawing should change — widen the tolerance if function allows, or add a fixture or a post-operation if it does not. Pushing the press harder to hit an impossible tolerance produces scrap and hides the real problem, which is usually a dimension that was copied from a metal part.