Cp and Cpk tell you whether a stable process can meet its specification, and how much margin it has. What the numbers mean, how to calculate and read them, and the common errors that make capability studies misleading.
A supplier reported a Cpk of 1.67 on a critical diameter, comfortably above the customer's requirement of 1.33. The customer's incoming inspection kept finding out-of-tolerance parts anyway. When the data was reviewed, the "study" had been run on 30 consecutive parts from one cavity during one hour of a perfect day. Over a normal week, across all four cavities, two material lots and three shifts, the real Cpk was about 0.9.
Capability indices are among the most quoted numbers in manufacturing quality, and among the most frequently misunderstood.
What capability means
A capable process consistently produces output within its specification limits. Capability compares two things:
- The voice of the customer: the specification width, from lower to upper limit.
- The voice of the process: the natural spread of the process, conventionally six standard deviations.
Cp: potential capability
Cp = (upper specification limit − lower specification limit) ÷ (6 × standard deviation)
Cp tells you whether the process spread would fit within the specification if it were perfectly centred. A Cp of 1.0 means the spread exactly fills the tolerance. A Cp of 2.0 means it takes half the tolerance.
Cpk: actual capability
Cpk = the smaller of (USL − mean) ÷ (3 × standard deviation) and (mean − LSL) ÷ (3 × standard deviation)
Cpk accounts for centring. A process with a great Cp but sitting near one limit will have a poor Cpk. The gap between Cp and Cpk tells you how much you would gain by centring the process, which is often much easier than reducing its variation.
What good looks like
Common guidelines:
- Cpk below 1.0: the process is producing, or will produce, out-of-specification parts. Containment needed.
- Cpk 1.0–1.33: marginal. Little room for drift.
- Cpk 1.33 or above: generally accepted as capable for ongoing production.
- Cpk 1.67 or above: often required for safety-critical characteristics and for new processes in automotive.
Pp and Ppk
Pp and Ppk use the overall standard deviation of all the data, including shift-to-shift and lot-to-lot variation, rather than the short-term within-subgroup variation used for Cp and Cpk. Ppk is a more honest picture of what the customer actually receives. A large gap between Cpk and Ppk shows that the process drifts over time.
Common errors
- Measuring capability on an unstable process. If a control chart shows special causes, capability numbers are meaningless. Stabilise first with SPC.
- Too little or unrepresentative data: a short run on one cavity, one shift or one material lot.
- Ignoring measurement error. A poor gauge inflates the apparent standard deviation, which is why Gauge R&R comes first.
- Assuming normality. Some characteristics, such as flatness, runout and concentricity, are naturally skewed. Use appropriate methods for non-normal data.
- Mixing cavities. Analyse each cavity separately as well as combined.
Using capability to improve
- Low Cpk, high Cp: centre the process.
- Low Cp: reduce variation, or question whether the specification is tighter than function needs.
- Cpk acceptable but Ppk poor: find and remove the sources of drift between shifts, lots or set-ups.
Capability is not a certificate to file away. It is a lens that shows where a process needs attention.
