Enter Process Inputs
Use raw measurements for automatic statistics, or enter mean and overall standard deviation directly.
Example Data Table
This example shows a stable characteristic with both specification limits and a central target.
| Observation | Measurement |
|---|---|
| 1 | 49.8 |
| 2 | 50.4 |
| 3 | 50.1 |
| 4 | 49.9 |
| 5 | 50.7 |
| 6 | 50.3 |
| 7 | 49.7 |
| 8 | 50.5 |
| 9 | 50.0 |
| 10 | 50.2 |
Example summary: LSL = 47, USL = 53, Target = 50, Mean ≈ 50.16, Overall standard deviation ≈ 0.34.
Formula Used
Pp measures total tolerance versus long term spread.
Pp = (USL − LSL) / (6 × s)
PPL and PPU measure one-sided performance.
PPL = (Mean − LSL) / (3 × s)
PPU = (USL − Mean) / (3 × s)
Ppk uses the weaker side.
Ppk = min(PPL, PPU)
Cpm also penalizes off-target behavior.
Cpm = (USL − LSL) / [6 × √(s² + (Mean − Target)²)]
PPM and yield assume a normal distribution.
PPM total = PPM below LSL + PPM above USL
Yield % = 100 − (PPM total / 10,000)
Here, s is the overall standard deviation estimated from all values, not the within-subgroup estimate.
How to Use This Calculator
- Enter a lower limit, upper limit, or both.
- Add a target when off-target loss matters.
- Paste raw measurements, or provide summary statistics.
- Choose the number of decimal places.
- Click Calculate Capability to view the result panel above the form.
- Use the export buttons to save the current result table as CSV or PDF.
Best practice: Use long term capability only after checking measurement quality, process stability, and rational sampling.
If your process is not stable, the indices may look precise while still misrepresenting future performance.
Frequently Asked Questions
1. What does long term capability measure?
It measures how well a process performs against specifications using overall variation collected across time, shifts, lots, and routine operating conditions.
2. What is the difference between Pp and Ppk?
Pp compares total spread with tolerance width. Ppk also considers how centered the process mean is, so it reflects actual long term performance more realistically.
3. When should I use raw measurements instead of summary statistics?
Use raw measurements whenever possible. They let the calculator estimate mean and overall standard deviation directly and reduce the risk of transcription mistakes.
4. Why is Ppk often lower than Pp?
Ppk drops when the process mean moves toward a limit. Even with small variation, poor centering weakens actual long term capability.
5. What does Cpm add to the analysis?
Cpm adjusts capability for deviation from the target. It is helpful when customer loss rises as the process drifts away from a desired value.
6. Are the PPM values exact?
No. They are estimated from a normal distribution model. If the data are skewed, mixed, or unstable, actual fallout can differ materially.
7. What Ppk value is usually considered good?
Many teams consider 1.33 acceptable and 1.67 strong, but required thresholds vary by industry, risk, customer expectations, and process maturity.
8. Can I use one-sided specifications?
Yes. The calculator supports a single upper or lower limit. In that case, one-sided performance becomes the main indicator of capability.