Process Capability (Cp/Cpk) Calculator

Process capability indices answer the question manufacturing quality teams care about most: not just whether a process is centered on target, but whether its natural variation is tight enough to reliably stay inside specification limits. Cp measures potential capability — the spec range divided by six standard deviations — and only asks whether the process's spread would fit inside the tolerance if it were perfectly centered; it ignores where the process actually sits. Cpk is the more honest, real-world number: it computes capability separately toward each spec limit (Cpu toward the upper limit, Cpl toward the lower) and reports the smaller of the two, so an off-center process gets penalized even if its spread alone would technically fit.

Cpm, the Taguchi index, goes a step further by folding the process mean's deviation from the exact midpoint of the spec range into the denominator, penalizing any drift from target even within otherwise acceptable limits. From Cpk, the calculator derives an estimated sigma level and defects-per-million using a polynomial approximation of the normal distribution's CDF, then maps the result to an industry-standard qualitative label — Cpk of 2.0+ is called Six Sigma/world class, 1.33+ is generally considered production-ready, and below 1.0 means the process isn't reliably capable regardless of how good it looks on paper. Two things worth knowing: these formulas all assume the underlying process data is normally distributed, which understates real defect rates for skewed distributions, and you should feed in within-subgroup (short-term) standard deviation rather than overall long-term sigma, since capability studies are conventionally calculated on short-term variation.