Cpk
Cpk (process capability index) measures how safely a process output fits inside its specification limits — accounting for both how spread out the process is and whether it's actually centered on target. Two processes can have identical spread and wildly different Cpk, purely because one of them is centered and the other isn't.
The formula captures exactly that "worse of the two sides" logic: Cpk = min[(USL − mean) / 3σ, (mean − LSL) / 3σ] — compute the distance from the process mean to each spec limit in units of 3 standard deviations, then take whichever side is tighter. A process that's drifted toward one limit gets penalized by that nearer limit, even if its overall spread (what Cp alone measures) hasn't changed at all. That's the entire difference between the two metrics: Cp measures capability assuming perfect centering; Cpk measures the capability you actually have, off-center drift included. Cpk can never exceed Cp — centering can only hurt, never help, relative to the idealized Cp number.
The index translates directly into a defect rate, which is why specific thresholds are contractual, not just descriptive:
| Cpk | Approximate defect rate |
|---|---|
| 1.00 | ~2,700 ppm (0.27%) |
| 1.33 | ~63 ppm |
| 1.67 | ~0.6 ppm |
| 2.00 (six-sigma) | ~0.002 ppm |
Semiconductor fabs set Cpk thresholds as hard qualification gates, not aspirational targets. A typical requirement is Cpk ≥ 1.33 for established production processes, rising to Cpk ≥ 1.67 for the most critical parameters — a process scoring below 1.0 is considered outright not capable, meaning a meaningful fraction of output will land outside spec and immediate corrective action is expected, not optional.
Calculating Cpk honestly requires real statistical discipline, not just plugging numbers into the formula. The process needs to be in verified statistical control — stable, not actively drifting — with enough data (typically 25+ subgroups) to estimate the mean and standard deviation reliably, and the underlying distribution needs to be reasonably close to normal for the 3σ math to mean what it claims to mean. A Cpk calculated from a short sampling window can overstate true capability; Ppk, calculated from long-term data that captures real process drift over time, is generally the more honest number for anything beyond an initial qualification snapshot.
Improving a low Cpk only has two real levers: tighten the spread, or recenter the mean. Reducing σ (the spread term) raises both Cp and Cpk together. Recentering the mean toward the midpoint between LSL and USL raises Cpk alone, closing the gap toward Cp without touching the process's underlying variation at all — often the faster, cheaper fix when a process is capable in principle but simply running off-target.