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Cpk calculator

Cpk (Process Capability Index) measures how well a manufacturing process fits within its specification limits, taking into account both the spread and the centering of the process. A higher Cpk means fewer defects and a more capable process.

While Cp only measures the spread of the process relative to the specification width, Cpk also accounts for how centered the process mean is within the tolerance band. A process can have a good Cp but a poor Cpk if it is shifted toward one of the specification limits.

Where x̄ is the process mean, σ is the process standard deviation, USL is the upper specification limit, and LSL is the lower specification limit.

Cpk vs Ppk: The formulas are identical — the difference is in σ. Cpk uses within-subgroup variation (short-term, requires subgroup data), while Ppk uses overall sample standard deviation (long-term, computed from all individual measurements). This calculator uses overall std from raw data, so it reports Ppk in raw-data mode and Cpk when you supply your own summary statistics.

Cpk and Ppk both measure process capability, but they use different estimates of standard deviation and serve different purposes. Cpk uses the within-subgroup standard deviation (often calculated from range or moving range), which captures only short-term, inherent process variation. Ppk uses the overall standard deviation calculated from all individual data points, which includes both short-term variation and any long-term shifts in the process mean.

Because of this difference, Cpk is almost always equal to or higher than Ppk. When Cpk and Ppk are close together, it means the process is stable — the mean is not drifting over time. When there is a large gap between them (e.g., Cpk = 1.8, Ppk = 1.2), it signals that the process mean is shifting between subgroups, and the process may not be in statistical control.

In practice, Cpk is used for short-term capability studies and initial process approval (such as PPAP submissions under IATF 16949). Ppk is used for long-term performance monitoring once the process is in production. Many automotive OEMs require both values, with Cpk ≥ 1.67 for PPAP and Ppk ≥ 1.33 for ongoing production. Always check your customer-specific requirements (CSRs) for the exact thresholds required.

Improving Cpk requires addressing two fundamental aspects of your process: centering (moving the mean closer to the target) and reducing variation (tightening the spread). The most effective approach depends on whether your Cpk is low because the process is off-center or because the variation is too large.

Center the process: If CPU and CPL are significantly different, your process mean is shifted toward one spec limit. Adjust machine offsets, tooling positions, or setpoints to move the mean toward the midpoint of the specification range. This is often the quickest and cheapest way to improve Cpk — a simple offset adjustment can yield dramatic results.

Reduce variation: If both CPU and CPL are low (meaning Cp itself is low), the process spread is too wide. Use root cause analysis tools — fishbone diagrams, 5-Why analysis, and designed experiments (DOE) — to identify the dominant sources of variation. Common culprits include material inconsistency, worn tooling, temperature fluctuations, and operator technique differences.

Verify measurement: Before investing in process changes, run a Gauge R&R study to confirm that your measurement system is not contributing excessive variation. A measurement system consuming more than 10% of the tolerance can make a capable process appear incapable. Fixing the measurement system first avoids chasing phantom variation in the process.

Consider a manufacturing process producing precision shafts with a diameter specification of 25.00 ± 0.20 mm (USL = 25.20 mm, LSL = 24.80 mm). After measuring 30 shafts from production, you find:

Step 1 — Calculate CPU and CPL:

CPU = (USL − x̄) / (3σ) = (25.20 − 25.02) / (3 × 0.048) = 0.18 / 0.144 = 1.25

CPL = (x̄ − LSL) / (3σ) = (25.02 − 24.80) / (3 × 0.048) = 0.22 / 0.144 = 1.53

Step 2 — Cpk is the minimum:

Cpk = min(CPU, CPL) = min(1.25, 1.53) = 1.25

Step 3 — Calculate Cp:

Cp = (USL − LSL) / (6σ) = (25.20 − 24.80) / (6 × 0.048) = 0.40 / 0.288 = 1.39

Interpretation: The Cpk of 1.25 is marginal — it falls between 1.00 and 1.33. The process is producing parts within spec, but with limited margin. Notice that Cp (1.39) is higher than Cpk (1.25), which tells us the mean is shifted slightly toward the USL (CPU is the limiting factor). By adjusting the process to center the mean at exactly 25.00 mm, Cpk would increase to match Cp at 1.39, bringing the process into the capable range.