Calculator Inputs
Example Data Table
Sample measurements for a 10.000 ± 0.200 requirement (illustrative only).
| # | Measurement | # | Measurement | # | Measurement |
|---|---|---|---|---|---|
| 1 | 10.01 | 2 | 9.99 | 3 | 10.03 |
| 4 | 10.00 | 5 | 10.02 | 6 | 9.98 |
| 7 | 10.04 | 8 | 10.01 | 9 | 10.00 |
| 10 | 9.97 | 11 | 10.02 | 12 | 10.03 |
Formulas Used
- Mean: μ = (Σxi) / n
- Std Dev (sample): s = √(Σ(xi−μ)² / (n−1))
- Cp: (USL − LSL) / (6s)
- CPU: (USL − μ) / (3s), CPL: (μ − LSL) / (3s)
- Cpk: min(CPU, CPL) (or the available side for one-sided specs)
- Estimated PPM out-of-spec: P(X<LSL) + P(X>USL), assuming normal distribution
How to Use This Calculator
- Enter LSL, USL, and an optional target.
- Choose Raw measurements to paste values, or Summary statistics if you already have mean and standard deviation.
- Pick a standard deviation method for raw data.
- Click Calculate to show results above the form.
- Use Download CSV or Download PDF for reporting.
FAQs
1) What does Cpk measure?
Cpk measures how well a process fits within specification limits, considering both spread and centering. Higher values mean fewer defects and more consistent output.
2) Why can Cp be higher than Cpk?
Cp reflects potential capability based only on variation. Cpk also accounts for how far the mean is from the nearest spec limit, so off-center processes reduce Cpk.
3) Can I calculate with only one spec limit?
Yes. For one-sided specs, the calculator reports Cpk using CPU or CPL, depending on which limit you provide. This is common for maximum weight or minimum strength requirements.
4) Should I use sample or population standard deviation?
Use sample (n−1) for typical measurement samples and subgroup data. Use population (n) when your data represents the full population or you follow an established internal standard.
5) Is the PPM estimate always accurate?
It assumes a stable, normally distributed process. If data is non-normal, autocorrelated, or contains special causes, use appropriate transformations or distribution fitting before relying on PPM.
6) What Cpk value is considered “good”?
Many teams use 1.33 as a baseline for capability and 1.67 for critical characteristics. Requirements vary by industry, risk, and customer expectations, so follow your control plan.
7) Why does my Cpk change after more samples?
More data improves estimates of mean and variation. Early small samples can over- or under-estimate standard deviation, so capability indices often shift until the process is well characterized.