Professional Guide
Process Capability (Cp/Cpk) Explained
How to judge whether a process can meet its specification: capability indices, what Cpk < 1 means, and how capability differs from simply being in control.
A process can be stable and still produce output that misses the specification. Process capability asks a different question: relative to the specification limits, can this process deliver acceptable output at all?
This guide explains the capability indices Cp and Cpk, how to calculate them, and how to interpret the numbers in engineering and manufacturing decisions.
Cp and Cpk defined
Cp measures how wide the specification is relative to the process spread: Cp = (USL − LSL) ÷ (6σ), where USL and LSL are the upper and lower specification limits and σ is the process standard deviation. It assumes the process is centred.
Cpk adjusts for the process being off-centre. It is the smaller of the two one-sided indices: Cpk = min((USL − mean) ÷ 3σ, (mean − LSL) ÷ 3σ). A centred process has Cp = Cpk; an off-centre process has Cpk < Cp.
Interpreting the numbers
A Cpk of 1.0 means the process is capable to within about 3 standard deviations of the nearest specification limit — roughly 2,700 defects per million opportunities if the process is stable. A Cpk of 1.33 is a common industry requirement, and 1.67 or higher is used for demanding applications.
The process-capability (Cp/Cpk) calculator takes the specification limits, mean and standard deviation and returns both indices. The standard-deviation calculator provides σ from your sample data.
Capability vs control — and what to fix first
Statistical control (a stable process) and capability (output within specification) are different. If a process is out of control, capability numbers are meaningless until the special causes are removed. If it is in control but not capable, you must change the process itself — narrow the spread or move the mean — not just monitor it.
Report the mean, standard deviation, specification limits and the capability index together so the numbers can be audited.
Key takeaways
- Cp compares specification width to process spread; Cpk also accounts for centring.
- Cpk = min((USL−mean)/3σ, (mean−LSL)/3σ); Cpk < 1 means part of the spec is outside ±3σ.
- Capability requires statistical control first — capability is meaningless for an unstable process.
- Common targets: Cpk ≥ 1.33 (general), ≥ 1.67 (demanding).
Tools used in this guide
Related guides
References
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