Cpk Calculator — Process Capability (Cp, Cpk, CPU, CPL)

Cpk — the process capability index — measures how well a process fits inside its specification limits, taking both its spread and its centering into account. It answers the practical question: given where the process mean sits and how much it varies, how much room is left before output crosses the nearest spec limit? A Cpk of 1.0 means the nearest limit sits exactly 3 standard deviations from the mean; higher is safer.

Its sibling Cp asks a simpler question: could the process fit the spec if it were perfectly centered? Cp compares the spec width to the process spread and ignores the mean entirely. That makes the pair diagnostic: Cp is the best-case capability, Cpk is the actual capability, and the gap between them is the cost of being off-center.

Cp = (USL − LSL) / 6σ

Cpk = min( (USL − μ) / 3σ , (μ − LSL) / 3σ )

μ is the process mean, σ the process standard deviation, and USL/LSL the upper and lower specification limits. The two terms inside the min() are CPU (capability against the upper limit) and CPL (against the lower limit) — Cpk is simply whichever side is worse. With a one-sided spec, CPU or CPL alone serves as the effective Cpk, and Cp is undefined because there is no spec width.

A filling line targets 500 ml with specs at 495–505 ml. A capability study finds the process mean at 501.5 ml with a standard deviation of 1.2 ml.

Cp  = (505 − 495) / (6 × 1.2)   = 10 / 7.2  = 1.39
CPU = (505 − 501.5) / (3 × 1.2) = 3.5 / 3.6 = 0.97
CPL = (501.5 − 495) / (3 × 1.2) = 6.5 / 3.6 = 1.81
Cpk = min(0.97, 1.81)           = 0.97

The spread would comfortably fit the spec (Cp = 1.39, better than the 1.33 standard), but the mean sits 1.5 ml high, so the upper tail is spilling defects: Cpk = 0.97 is below even the marginal 1.0 line. The fix is centering, not variation reduction — shifting the mean back to 500 ml would lift Cpk to ≈ 1.39 with no other change to the process.

Cpk ≥ 1.33 is the acceptance convention most industries and customer PPAP requirements use: it leaves a full standard deviation of margin between the process and its nearest limit. Below 1.0, a meaningful share of output is already outside spec.

Read Cp and Cpk together. If both are low, the process varies too much for the spec — reduce variation. If Cp is healthy but Cpk lags well behind it, the spread is fine and the process is simply off-center — recentering the mean is usually the cheapest capability gain available. If Cp and Cpk are nearly equal, the process is well-centered and any further gain has to come from tightening variation.

Two prerequisites before trusting any capability index: the process must be stable (in statistical control — check a control chart first, because capability of an unpredictable process is meaningless), and the data should be approximately normal, since the indices and the PPM estimate assume a normal distribution. Also mind the short-term vs long-term distinction: computed from within-subgroup variation these formulas give Cp/Cpk (potential capability); computed from overall long-term standard deviation they give Pp/Ppk (actual performance). This calculator applies whichever σ you enter — label your result accordingly.