Calculate process capability index with statistical precision, sample distributions, and inference data.
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C_{pk} = \min\left(\frac{USL - \mu}{3\sigma}, \frac{\mu - LSL}{3\sigma}\right), \quad C_p = \frac{USL - LSL}{6\sigma}CpCpkUSL, LSLμ, σ“Evaluate the capability of a precision machining shaft diameter process with USL = 105.0 mm, LSL = 95.0 mm, process mean μ = 100.5 mm, and std dev σ = 1.2 mm.”
Cp reflects the spread of the process independent of where it is centered.
Cpu gauges proximity to the upper spec; Cpl gauges proximity to the lower spec.
Cpk is the minimum of Cpu and Cpl.
The process is moderately capable (Cpk > 1.0) but shifted slightly high towards the upper tolerance limit, generating ~88 parts per million out of specification.
| Input Scale | Standard Output Range | Variance Band | Recommendation |
|---|---|---|---|
| Low Baseline | 0.00 – 25.00 | ±1.5% | Optimal for conservative estimations |
| Median / Standard | 25.00 – 100.00 | ±0.8% | Benchmark standard for commercial workflows |
| Elevated / High | 100.00 – 500.00 | ±0.4% | Recommended for high-throughput modeling |
| Extreme Maximum | > 500.00 | ±0.1% | Verify input constraints for boundary saturation |
Provide your numeric inputs into the designated fields in Process Capability Index Calculator.
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Cp measures the potential capability assuming the process mean is perfectly centered between specifications (Tolerance / 6σ). Cpk accounts for process centering drift by evaluating the distance from the mean to the nearest tolerance boundary. If a process is centered, Cp = Cpk; if shifted, Cpk < Cp.
A Cpk < 1.0 means the 3-sigma process spread exceeds one or both specification limits, resulting in active production of non-conforming or defective items that require immediate tooling adjustment or scrap inspection.
Using standard normal cumulative distribution Φ(z), where Z_upper = 3·Cpu and Z_lower = 3·Cpl, the expected fractional defect is [1 - Φ(Z_upper)] + [1 - Φ(Z_lower)]. Multiplying by 1,000,000 yields Parts Per Million (PPM).
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