Cpk Calculator — Process Capability (Cp, Cpk, PPM & Yield)

Capability compares the voice of the process — how much your parts naturally vary — against the voice of the customer, the tolerance band on the drawing. Cp = (USL − LSL) ÷ 6σ asks the first question: is the process spread narrow enough to fit inside the tolerance at all? A Cp of 1.0 means the natural spread exactly fills the band with nothing to spare; 1.33 means the band is a third wider than the spread, the usual minimum many customers ask for; 1.67 and 2.0 are the tighter automotive and six-sigma targets. But Cp assumes the process is perfectly centred, which real processes never are.

Cpk is the honest one because it accounts for where the process is actually sitting. It measures the distance from the mean to the nearer spec limit in units of 3σ: Cpk = min[(USL − x̄), (x̄ − LSL)] ÷ 3σ. If the process is drifting toward one limit, Cpk drops below Cp and tells you the truth that Cp hides. When the process is perfectly centred, Cpk equals Cp; the gap between them is a direct measure of how far off-centre you are running, and often the cheapest capability improvement available is simply re-centring the mean rather than reducing variation.

The reason capability is expressed as a single index is that it maps straight onto a reject rate. A centred process at Cpk 1.00 puts each spec limit at 3σ from the mean, which is about 2700 parts-per-million outside — roughly a quarter of a percent scrap. Cpk 1.33 is about 63 PPM; Cpk 1.67 about 0.6 PPM. Each third of a point of Cpk is worth an order of magnitude in defect rate, which is why customers specify it rather than a percentage: it is a compact, comparable way to say how much margin a process is really running with. This tool shows the PPM and yield alongside the index so the connection is visible.

Feeding it raw measurements is the more useful mode for a first article or a PPAP study. Paste the values off the gauge and the tool computes the sample mean and the sample standard deviation (dividing by n − 1, the unbiased estimator) before working the capability — so you are not asked to calculate sigma by hand. Bear in mind that a handful of readings gives a shaky estimate of sigma; capability studies conventionally want 30-plus data points, ideally in rational subgroups over time, before the number means much.

The load-bearing caveat, said plainly: capability assumes a stable, normal process. If the data are not in statistical control — if there are trends, steps or outliers from tool wear, a re-fixture or a material change — then σ is not a meaningful description of the process and neither is Cpk. The index will happily compute a confident number from unstable data and it will be fiction. Plot the values in order first; if they are not behaving as one consistent population, fix that before trusting any capability figure. If you need a capability study run properly on a real part, that is exactly the kind of thing our inspection room does — send the drawing.