Capability indices compress a whole process into a single number a customer can ask for — "send me your Cpk". That convenience hides a lot, and the indices are routinely misused. Here is what each one measures, and when it means nothing at all.
What capability compares
Process capability compares the voice of the process — how much your output naturally spreads — with the voice of the customer — the tolerance you are allowed. A capable process fits comfortably inside its specification; an incapable one does not, however stable it is. Capability is only valid when the process is in statistical control — the mistake at the end that undoes everything.
Cp — potential capability
Cp = (USL − LSL) / 6σ. It asks a simple question: is the tolerance band wide enough to hold six standard deviations of process spread? A Cp of 1.0 means the spread exactly fills the tolerance; 1.33 means the tolerance is a third wider than the spread, giving you margin.
Cp's blind spot is that it ignores centring. It compares widths only, so a process can post a healthy Cp while sitting so far off-centre that it is making scrap. That is what Cpk fixes.
Cpk — actual capability
Cpk = the smaller of (USL − μ) / 3σ and (μ − LSL) / 3σ. By measuring from the process mean to each specification limit separately and taking the worse of the two, Cpk penalises a process for being off-centre. If Cp and Cpk are close, the process is well centred. If Cpk is much lower than Cp, you have a centring problem you can often fix by simple adjustment — the cheapest capability gain there is.
The common bar is Cpk ≥ 1.33 for a capable process, rising to ≥ 1.67 for safety-critical or special characteristics. A Cpk of 1.33 on a well-centred process corresponds to only a few tens of parts-per-million out of spec — as long as it stays in control.
Pp and Ppk — performance over the long run
Pp and Ppk use identical formulas with one change: the overall, long-term standard deviation of all the data, rather than the within-subgroup spread that Cp and Cpk use. Cp and Cpk describe what the process can do at its best, moment to moment; Pp and Ppk describe how it actually performed across all the drift and shifts of the full run. The gap between them is a useful diagnostic — a healthy Cpk but a poor Ppk means a process that is capable instant-to-instant but wandering over time.
The warning that undoes all of it
Every one of these indices assumes a stable, in-control, roughly normal process. Calculate Cpk on a process that is out of control and the number is not merely optimistic — it is meaningless, because an unstable process has no single spread or mean to measure. Control first, capability second, always. And if your data is visibly skewed or bounded — flatness, roundness, contamination counts — check normality before trusting the ppm figures, because non-normal data needs a transformation or a different method.
The order is not negotiable: bring the process into statistical control, then measure capability. Reverse it and you are quoting a number built on sand.
The free Cpk Calculator does the arithmetic — paste your measurements and specification limits and it returns Cp, Cpk and the predicted yield. For the control-first half of the job, the SPC Control Chart Toolkit builds the charts that prove stability, and Control charts explained covers why that has to come first.