Process Capability (Cpk) Calculator
Calculate process capability indices (Cp and Cpk) to determine how well your process fits within specification limits.
Results will appear here.
Formulas Used
Cp (Potential / Process Spread Capability):
Cp = (USL − LSL) / (6σ)
Measures whether the process spread fits within the specification width, ignoring centering.
Cpu (Upper Capability Index):
Cpu = (USL − μ) / (3σ)
Cpl (Lower Capability Index):
Cpl = (μ − LSL) / (3σ)
Cpk (Actual / Centered Capability):
Cpk = min(Cpu, Cpl)
Accounts for both spread and centering. Always ≤ Cp.
Centering Factor k:
k = |μ − midpoint| / ((USL − LSL) / 2)
Relationship: Cpk = Cp × (1 − k)
Capability Benchmarks:
| Cpk Value | Rating | Sigma Level |
|---|---|---|
| ≥ 1.67 | Excellent (Six Sigma) | 5σ+ |
| ≥ 1.33 | Capable | 4σ |
| ≥ 1.00 | Marginal | 3σ |
| < 1.00 | Incapable | <3σ |
Assumptions & References
- The process output is assumed to follow a normal (Gaussian) distribution.
- The process must be in statistical control (stable over time) for Cpk to be meaningful.
- σ should be the within-subgroup standard deviation (short-term) for true capability; using overall σ gives a performance index (Ppk).
- Both USL and LSL are required; for one-sided specs use only Cpu or Cpl respectively.
- PPM and % out-of-spec estimates use the standard normal CDF approximation (Horner's method).
- Industry standard: Cpk ≥ 1.33 is the minimum acceptable for most manufacturing processes; Cpk ≥ 1.67 for safety-critical parts.
- References: Montgomery, D.C. Introduction to Statistical Quality Control, 7th ed.; AIAG SPC Manual, 2nd ed.