Enter Process Data
Use within variation for short-term capability. Add overall variation for long-term performance and defect estimation. At least one limit is required.
Example Data Table
This sample shows typical inputs for a centered process with moderate long-term drift.
| Input Item | Example Value | Why It Matters |
|---|---|---|
| Process Mean | 50.12 | Shows where the process is actually running. |
| Within Standard Deviation | 0.42 | Measures short-term repeatability inside routine production. |
| Overall Standard Deviation | 0.51 | Captures longer-term drift and change across time. |
| Lower Specification Limit | 49.00 | Defines the lowest acceptable output value. |
| Upper Specification Limit | 51.00 | Defines the highest acceptable output value. |
| Target | 50.00 | Helps assess centering and loss from off-target running. |
| Sample Size | 125 | Supports confidence in the estimated statistics. |
| Batch Size | 10,000 | Converts reject rate into expected defect count. |
Formula Used
These equations compare your process spread and centering against the tolerance band. Capability improves when variation falls and centering improves.
Cp and Cpk
Cp = (USL - LSL) / (6 × within sigma)
Cpu = (USL - mean) / (3 × within sigma)
Cpl = (mean - LSL) / (3 × within sigma)
Cpk = minimum of Cpu and Cpl
Pp and Ppk
Pp = (USL - LSL) / (6 × overall sigma)
Ppu = (USL - mean) / (3 × overall sigma)
Ppl = (mean - LSL) / (3 × overall sigma)
Ppk = minimum of Ppu and Ppl
Cpm and Centering
Cpm = (USL - LSL) / (6 × √(within sigma² + (mean - target)²))
Center Shift = mean - midpoint of specifications
Yield and Defects
Lower reject = Φ((LSL - mean) / overall sigma)
Upper reject = 1 - Φ((USL - mean) / overall sigma)
Total reject = lower reject + upper reject
Yield = 1 - total reject
PPM = total reject × 1,000,000
How to Use This Calculator
- Enter the process mean from your measured production sample.
- Add the within standard deviation for short-term capability values.
- Enter the overall standard deviation when you want long-term performance metrics.
- Fill in the lower limit, upper limit, or both depending on your specification type.
- Provide a target when centering and target loss matter.
- Add sample size and batch size for richer interpretation.
- Press Calculate Capability to show the results above the form.
- Use the CSV or PDF buttons to save the results for reports.
Frequently Asked Questions
1. What does Cpk tell me?
Cpk shows how close your process mean is to the nearest specification limit after considering short-term spread. Higher values indicate stronger routine capability.
2. Why are Cp and Cpk different?
Cp measures potential capability from spread alone. Cpk also reflects centering, so it drops when the process drifts toward one limit.
3. When should I use Ppk instead of Cpk?
Use Ppk when you want long-term performance using overall variation. It captures drift, shift changes, setup changes, and other time-based effects.
4. What Cpk value is considered good?
Many teams treat 1.33 as capable and 1.67 as strong. Actual targets depend on risk, customer requirements, and process criticality.
5. Why does the calculator estimate yield?
Yield translates capability into expected conforming output. It helps connect statistics with customer impact, waste, rework, and defect planning.
6. Can I use one-sided specifications?
Yes. Leave one limit blank when only an upper or lower boundary matters. The calculator will use the available side for index calculations.
7. Why do results depend on normality?
Yield and PPM estimates use the normal distribution. Strong skew, mixtures, or unstable data can make defect predictions less reliable.
8. What should I do if Cp is high but Cpk is low?
Your spread may be acceptable, but the process is off-center. Focus on centering the mean before investing in variation reduction.