Cp, Cpk, Pp & Ppk calculator
Calculate two-sided capability or performance indices from specification limits, mean and an explicitly selected variation estimate.
Result
Inputs used
- Lower specification limit
- 9.5
- Upper specification limit
- 10.5
- Process mean
- 10.1
- Standard deviation
- 0.1
- Variation estimate
- Within-subgroup: Cp / Cpk
| Cp | 1.666667 |
|---|---|
| Cpk | 1.333333 |
| Distance to nearest specification | 0.4 measurement units |
Two-sided specification only. Normal-distribution interpretation requires stable, representative data and a suitable measurement system. Negative Cpk/Ppk means the mean is outside specification. No universal pass threshold is assumed.
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Formula and worked example
Cp = (USL − LSL) / (6 × within-subgroup sigma). Cpk = min(USL − mean, mean − LSL) / (3 × within-subgroup sigma). Selecting overall standard deviation labels the corresponding results Pp and Ppk.
For limits 9.5 and 10.5, mean 10.1 and sigma 0.1, the indices are 1.6667 and 1.3333. Centering the mean at 10.0 makes both 1.6667 without reducing variation. These numbers are illustrative; acceptance criteria belong to the product and customer agreement.
Choose the variation estimate deliberately
A standard deviation calculated from all observations is an overall estimate. It is not automatically a within-subgroup estimate. Use the sample statistics calculator for an overall sample summary, then choose the overall option here. Preserve subgroup and time information when investigating short-term capability.
This tool accepts two specification limits. Specifications are engineering requirements; control limits are estimates of process behavior. They are not interchangeable. Stable and representative data, an adequate measurement system and an appropriate distribution model are prerequisites for interpreting indices.
Frequently asked questions
Can Cpk be negative?
Yes. A negative value means the process mean lies outside at least one specification limit. The tool preserves that result.
Does a high index prove the process is in control?
No. A summary index cannot establish stability, sampling independence or measurement quality. Review the time sequence and control charts.
Reference
NIST: process capability explains the indices and their normal-distribution assumptions.
Go deeper
Cite this page: Cp, Cpk, Pp & Ppk calculator
, Shopfloor. https://shopfloor.space/tools/process-capability-calculator/