Cpk
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Cpk is a process capability index that measures how well a process performs relative to specification limits, accounting for both variation and centering.
Definition
Cpk (Process Capability Index) is a statistical measure that indicates how well a process meets specification requirements, accounting for both the spread of the process and its centering relative to specification limits. Unlike Cp, which only measures potential capability, Cpk reveals actual capability by considering how close the process mean is to the nearest specification limit. A Cpk of 1.0 means the process edge just touches the nearest spec limit; 1.33 provides a safety margin; 2.0 represents Six Sigma-level performance.
Examples
A bottling line targets 500mL with spec limits of 495-505mL. The process mean is 502mL with standard deviation of 1.2mL. Cpk = min[(505-502)/(3×1.2), (502-495)/(3×1.2)] = min[0.83, 1.94] = 0.83. Despite low variation, the off-center mean limits capability. Recentering to 500mL would raise Cpk to 1.39.
Key Points
- Cpk formula: minimum of (USL - mean) / 3σ and (mean - LSL) / 3σ
- Cpk ≤ 1.0 indicates defects are being produced
- Cpk = 1.33 is the common minimum standard for capable processes
- Cpk = 2.0 corresponds to Six Sigma performance (3.4 DPMO)
Common Misconceptions
Cpk and Ppk are interchangeable. Cpk uses within-subgroup variation (short-term capability); Ppk uses total variation (long-term performance). Cpk shows what the process could do if stable; Ppk shows what it actually does over time. Both are needed.
A high Cpk means no defects. Even Cpk of 2.0 allows 3.4 defects per million. For ultra-critical applications (aerospace, medical devices), higher Cpk targets may be required. Context determines the appropriate capability target.