Statistical
Process capability Cp and Cpk: spread and centering
Measure manufacturing spread Cp = (USL - LSL)/(6*SD) and off-center capability Cpk = MIN((USL - Mean)/(3*SD), (Mean - LSL)/(3*SD)).
Why Cp = 1.67 can still ship defects if Cpk = 0.83 (centering matters!)
Cp compares the specification interval with six standard deviations. Cpk also measures the mean distance to the nearer limit. Use a stable process, an appropriate sigma estimate, and a suitable distributional model before interpreting these indices.
For limits 9.90 and 10.10 with sigma 0.02, Cp is 1.6667. Moving the mean to 10.05 leaves Cp unchanged but reduces Cpk to 0.8333. A mean outside the specification interval gives negative Cpk. Acceptance thresholds depend on the customer and application; these numbers do not establish IATF certification or a universal production-release rule.
| Capability Metric (LSL=9.90, USL=10.10, SD=0.02) | Mean = 10.00 (Centered) | Mean = 10.05 (Drifted!) |
|---|---|---|
| Potential Capability Cp | 1.6667 | 1.6667 (Blind to drift!) |
| Upper Cpu = (USL - Mean)/(3*SD) | 1.6667 | 0.8333 (Only 2.5σ to USL!) |
| Cpk | 1.6667 (centered) | 0.8333 (off-center) |
Centered Process Capability Cpk and Potential Capability Cp formulas
MIN(Cpu, Cpl) automatically identifies the tighter spec wall (upper or lower).
=IF(OR(COUNT(A2:D2)<>4,B2<=A2,D2<=0),"Invalid inputs",ROUND(MIN((B2-C2)/(3*D2),(C2-A2)/(3*D2)),4))Potential Process Capability Cp (assuming perfect centering)
Cp describes the potential index at the midpoint if the spread remains unchanged. Re-centering a real process can change its spread, so the difference is not a guaranteed improvement. Specify how sigma was estimated: within-process and overall variation are not interchangeable.
=IF(OR(COUNT(A2:D2)<>4,B2<=A2,D2<=0),"Invalid inputs",ROUND((B2-A2)/(6*D2),4))Try the example
Use the original values or change them to test your understanding.