Calculator Inputs
Example Data Table
| Sample | Measured value | Status |
|---|---|---|
| 1 | 49.92 | Within specification |
| 2 | 50.04 | Within specification |
| 3 | 50.10 | Within specification |
| 4 | 49.98 | Within specification |
| 5 | 50.16 | Within specification |
| 6 | 50.03 | Within specification |
| 7 | 50.07 | Within specification |
| 8 | 50.11 | Within specification |
Formula Used
Cp = (USL − LSL) / (6 × σwithin)
Cpu = (USL − μ) / (3 × σwithin)
Cpl = (μ − LSL) / (3 × σwithin)
Cpk = minimum(Cpu, Cpl)
Pp and Ppk use the same structure with σoverall for long-term capability.
Cpm = (USL − LSL) / [6 × √(σoverall2 + (μ − target)2)]
Expected ppm is estimated from the normal distribution tails beyond the specification limits.
How to Use This Calculator
- Select manual statistics when you already know the mean and sigma values.
- Select measurement dataset when you want the page to calculate statistics from raw observations.
- Enter the lower and upper specification limits exactly as defined by engineering requirements.
- Add the target value if you want the page to report Cpm.
- Choose the within sigma estimator that matches your study method.
- Press the calculate button to display results above the form.
- Use the export buttons to download the result summary as CSV or PDF.
Frequently Asked Questions
1. What is the difference between Cp and Cpk?
Cp measures potential capability using spread only. Cpk also checks centering, so it drops when the process mean drifts toward either specification limit.
2. When should I use dataset mode?
Use dataset mode when you have raw measurements and want the page to estimate mean, sigma, yield, and long-run capability directly from observations.
3. Why can Cp be higher than Cpk?
That happens when spread is acceptable but the mean is not centered. Cp ignores mean location, while Cpk reflects the closest specification side.
4. What Cpk value is usually considered acceptable?
Many engineering teams treat 1.33 as a practical minimum. Critical processes often target 1.67 or higher for stronger quality margins.
5. What does the k index show?
k measures off-centering relative to the tolerance midpoint. A value near zero indicates a centered process, while higher values indicate drift.
6. Why are Pp and Ppk included?
They represent overall or long-term performance using overall sigma. Comparing Cp with Pp helps you see whether extra variation appears over time.
7. What does expected ppm mean?
Expected ppm estimates how many parts per million may fall outside specifications if the process follows a normal distribution with the calculated sigma.
8. Does this page replace a full capability study?
No. It is a fast evaluation tool. Formal studies should still verify stability, normality, measurement quality, subgrouping, and sampling strategy.