Cpk Process Capability Calculator
Turn spec limits and a stable sample into Cp, Cpk and an estimated defect rate, so you can tell whether a process is capable or just lucky. Your numbers stay in your browser.
Process capability (Cpk)
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How this is calculated
Capability indices compare how wide your specification window is against how much your process actually varies. A capable process fits comfortably inside its limits.
Cpl = (mean − LSL) ÷ (3 × sigma)
Cpk = the smaller of Cpu and Cpl
The estimated defect rate uses the standardized distance from the mean to each spec limit and the normal distribution tail beyond it. The calculator implements an accurate rational approximation of the error function to compute those tails.
DPMO ≈ 1,000,000 × ( tail(z_upper) + tail(z_lower) )
where tail(z) = 1 − Φ(z), the area beyond z under a standard normal
A rough sigma level is reported as three times Cpk, the common shorthand that links capability to a short-term sigma rating.
Cp versus Cpk, and what this assumes
- Cp ignores centering. Cp only asks whether the spread could fit; Cpk also asks whether the process is centered. When the mean sits dead center, Cp and Cpk are equal. As the mean drifts toward a limit, Cpk falls while Cp stays put.
- Normality is assumed. The DPMO estimate assumes the characteristic is normally distributed. Skewed, bounded, or multimodal data will make the tail estimate misleading.
- Stability comes first. Capability only means something for a process that is in statistical control. If the process is drifting or unstable, no single Cpk describes it honestly.
- Sigma quality matters. Use a sigma estimated from a rational subgroup approach, not a mixed sample, or capability will look better or worse than reality.
Capability tells you whether a process can hold spec; yield tells you what actually got through. Pair this with the first pass yield and RTY calculator and price the fallout with the cost of quality calculator. For the improvement system around it, see lean manufacturing.
Make capability visible in real time
Harmony connects your machines, gauges, and quality records into one real-time operational layer, no rip-and-replace, so drift toward a spec limit shows up as it happens instead of in next month's capability study. Read the CLS case study.
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