PPM Trend Plot
This graph shows the estimated ppm response across a range of nearby Cpk values using your selected specification mode and sigma shift.
Calculator Inputs
Enter a Cpk value and choose how you want the defect estimate modeled.
Example Data Table
These example values use the same formulas as the calculator. Values are rounded for readability.
| Cpk | Mode | Sigma Shift | Estimated PPM | Estimated Yield % |
|---|---|---|---|---|
| 0.67 | Two-Sided | 0.0 | 44,431.1889 | 95.5569 |
| 1.00 | Two-Sided | 0.0 | 2,699.7961 | 99.7300 |
| 1.33 | Two-Sided | 0.0 | 66.0733 | 99.9934 |
| 1.67 | One-Sided | 0.0 | 0.2722 | 99.99997 |
| 2.00 | Two-Sided | 1.5 | 6.7953 | 99.9993 |
Formula Used
The calculator first converts Cpk to a sigma distance:
Z = 3 × Cpk
When a sigma shift is selected, the adjusted sigma distance becomes:
Zadjusted = Z − Sigma Shift
For a one-sided estimate:
PPM = [1 − Φ(Zadjusted)] × 1,000,000
For a two-sided estimate under a centered-process assumption:
PPM = 2 × [1 − Φ(Zadjusted)] × 1,000,000
Estimated yield is:
Yield % = [1 − (PPM / 1,000,000)] × 100
Approximate DPMO is:
DPMO ≈ PPM × Opportunities per Unit
Expected defective units in the chosen batch are:
Expected Defective Units = Batch Size × (PPM / 1,000,000)
Approximate expected total defects are:
Expected Defects ≈ Batch Size × Opportunities × (PPM / 1,000,000)
How to Use This Calculator
- Enter the known Cpk value from your capability study.
- Select whether your process is two-sided or one-sided.
- Choose a sigma shift if your method uses a long-term shift assumption.
- Enter opportunities per unit if you also want an approximate DPMO value.
- Enter your batch size to estimate defective units and total defects.
- Pick the number of decimal places to display.
- Click Calculate Now to show the results above the form.
- Use Download CSV or Download PDF to export the output.
Frequently Asked Questions
1) What does Cpk measure?
Cpk measures how well a process fits within specification limits while considering process centering. Higher Cpk values usually indicate fewer expected defects and stronger capability.
2) Is ppm from Cpk always exact?
No. This conversion is an estimate. Exact defect probability also depends on distribution shape, centering, stability, and whether both tails behave symmetrically.
3) When should I use one-sided mode?
Use one-sided mode when only one limit matters, such as a maximum impurity level or a minimum strength requirement. It estimates one tail instead of two.
4) Why is sigma shift included?
Some quality systems model long-term performance by reducing the effective sigma level. The shift option lets you compare unshifted and shifted defect estimates quickly.
5) What is the difference between PPM and DPMO?
PPM usually refers to defective units per million. DPMO refers to defects per million opportunities and considers how many possible defect chances exist in each unit.
6) What is considered a good Cpk?
Many industries view 1.33 as capable, 1.67 as strong, and 2.00 as excellent. Acceptance targets vary by product risk, customer needs, and regulation.
7) Can Cpk be below zero?
Yes. A negative Cpk can happen when the process mean lies beyond a specification limit. That indicates severe capability failure and very high expected defects.
8) When should I avoid Cpk-only conversion?
Avoid Cpk-only conversion when the process is highly off-center, non-normal, unstable, or strongly skewed. In those cases, use actual mean, sigma, and distribution analysis.