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Process Capability Index (Cp / Cpk) Calculator

Compute the process capability indices Cp and Cpk from spec limits and a mean & standard deviation (or raw measurement data), with a rating to interpret the result.

Input

How to provide mean & standard deviation

Result

Process capability index Cpk

1.111

Rating: Slightly low

Minimum capability is met, but tighter control is recommended.

Cp (potential)

1.111

Cpk (actual)

1.111

Bias factor k

0.000

Calculation breakdown

Upper spec limit (USL)10.5000
Lower spec limit (LSL)9.5000
Spec width (USL − LSL)1.0000
Spec center10.0000
Mean10.0000
Standard deviation (σ)0.15000
Upper (USL − mean)/(3σ)1.111
Lower (mean − LSL)/(3σ)1.111

How it works

  • Cp (process capability index) measures how small the variation is relative to the spec width: Cp = (USL − LSL) ÷ (6 × standard deviation σ). It reflects the potential capability assuming the mean sits at the spec center.
  • Cpk is the actual capability accounting for an off-center mean: Cpk = min((USL − mean), (mean − LSL)) ÷ (3σ). The further the mean drifts from the spec center, the smaller Cpk becomes compared with Cp.
  • Common rating thresholds: a Cpk of 1.33 or higher means capability is sufficient (good), 1.00–1.33 is slightly low, below 1.00 is prone to defects and needs improvement, and 1.67 or higher is considered excess capability.
  • When deriving the standard deviation from data, "sample (divide by n−1)" gives the sample standard deviation used to estimate the population, while "population (divide by n)" describes the variation of the data at hand. Process capability evaluation typically uses n−1.
  • The bias factor k indicates how far the mean is offset from the spec center: k = |spec center − mean| ÷ (spec width ÷ 2). The larger k is, the wider the gap between Cp and Cpk.
  • Results from this tool are estimates. A formal capability assessment should assume normality of the data and a stable, in-control process (verified with a control chart).