Measurement Data & Specifications
Process Capability Results
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What is Process Capability?
Process capability is a statistical measure that compares the output of a process against its specification limits. It quantifies how well a process can produce output within the acceptable range defined by engineering or customer requirements. The most common indices are Cp, Cpk, Pp, and Ppk.
Cp and Cpk use the within-subgroup (short-term) standard deviation, estimated from control chart methods such as R-bar/d2. They reflect the inherent capability of the process when it is in statistical control.
Pp and Ppk use the overall (long-term) standard deviation calculated directly from all data points. They reflect the actual performance of the process, including any shifts and drifts over time.
How to Calculate Cpk
Cpk is the minimum of the upper and lower capability ratios. It tells you how close the process mean is to the nearest specification limit, normalized by the process spread:
Cpk = min[ (USL − X̄) / (3 × σwithin) , (X̄ − LSL) / (3 × σwithin) ]
Where USL and LSL are the upper and lower specification limits, X̄ is the process mean, and σwithin is the within-subgroup standard deviation estimated as R̄ / d2.
Cp vs Cpk
Cp measures only the process spread relative to the specification width. It assumes the process is perfectly centered and is calculated as:
Cp = (USL − LSL) / (6 × σwithin)
Cpk accounts for both spread and centering. A process can have a high Cp (narrow spread) but a low Cpk if the mean has shifted toward one specification limit. If Cp = Cpk, the process is perfectly centered. If Cpk < Cp, the process mean is off-center.
Pp vs Ppk (Short-term vs Long-term)
The key difference between capability (Cp/Cpk) and performance (Pp/Ppk) indices is the sigma estimate used:
- Cp / Cpk use within-subgroup sigma (σwithin = R̄ / d2), capturing only short-term, inherent variation.
- Pp / Ppk use overall sigma (the sample standard deviation of all measurements), capturing total variation including between-subgroup shifts.
When a process is in statistical control, Cp ≈ Pp and Cpk ≈ Ppk. A large gap between Cpk and Ppk signals that the process mean is shifting between subgroups, which is an opportunity for improvement.
Cpk Benchmarks
| Cpk Value | Rating | Interpretation |
|---|---|---|
| < 1.00 | Process does not meet specifications. Significant defects expected. | |
| 1.00 – 1.33 | Process barely meets specifications. Tight monitoring required. | |
| 1.33 – 1.67 | Process comfortably meets specifications. Typical manufacturing target. | |
| > 1.67 | Process is highly capable. Suitable for critical-to-quality characteristics. |
When to Use Cp, Cpk, Pp, Ppk
Choosing the right index depends on your analysis goals:
- Use Cp when you want to understand the potential capability of a centered process (best-case scenario).
- Use Cpk as the primary short-term capability metric. It is the most commonly reported index and accounts for process centering.
- Use Pp to compare overall process spread against specifications without regard to centering.
- Use Ppk for long-term performance assessment, especially during initial process studies or when analyzing historical data that may include process shifts.
For ongoing SPC, report Cpk from control-charted data. For initial capability studies or process qualification, report both Cpk and Ppk to distinguish inherent capability from actual performance.