Process Capability (Cp & Cpk) Calculator
This calculator helps professionals calculate the Process Capability indices (Cp and Cpk) to gauge how well a process is performing relative to its specification limits. It is tailored for quality engineers, production managers, and Six Sigma practitioners.
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Data Source and Methodology
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti dal manuale "Quality Control Handbook" by Juran and Gryna.
The Formula Explained
\[ Cp = \frac{USL - LSL}{6 \cdot \sigma} \]
\[ Cpk = \min \left( \frac{USL - \mu}{3 \cdot \sigma}, \frac{\mu - LSL}{3 \cdot \sigma} \right) \]
Glossary of Variables
- Mean (\(\mu\)): The arithmetic average of a set of numbers.
- Standard Deviation (\(\sigma\)): A measure of the amount of variation or dispersion in a set of values.
- USL: Upper Specification Limit, the maximum acceptable value.
- LSL: Lower Specification Limit, the minimum acceptable value.
How It Works: A Step-by-Step Example
Suppose a process has a mean (\(\mu\)) of 50, a standard deviation (\(\sigma\)) of 2, a USL of 56, and an LSL of 44. The Cp value would be calculated as follows:
The Cpk value would be calculated using the minimum of two calculations:
Frequently Asked Questions (FAQ)
What is the Cp index?
Cp is a measure of a process's potential capability to meet specification limits.
What is the Cpk index?
Cpk is a measure of a process's actual capability to produce output within specification limits.
How do I interpret Cp and Cpk values?
A Cp or Cpk value less than 1 indicates the process is not capable of producing within specification limits.
Why is Cpk important?
Cpk considers both the process mean and variation, providing a more accurate representation of process capability.
Can Cp be greater than Cpk?
Yes, Cp can be greater than Cpk if the process mean is not centered between the specification limits.
Formula (LaTeX) + variables + units
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Cp = \frac{USL - LSL}{6 \cdot \sigma}
Cpk = \min \left( \frac{USL - \mu}{3 \cdot \sigma}, \frac{\mu - LSL}{3 \cdot \sigma} \right)
Cp = \frac{56 - 44}{6 \cdot 2} = 1
Cpk = \min \left( \frac{56 - 50}{3 \cdot 2}, \frac{50 - 44}{3 \cdot 2} \right) = 1
\[ Cp = \frac{USL - LSL}{6 \cdot \sigma} \] \[ Cpk = \min \left( \frac{USL - \mu}{3 \cdot \sigma}, \frac{\mu - LSL}{3 \cdot \sigma} \right) \]
\[ Cp = \frac{56 - 44}{6 \cdot 2} = 1 \]
\[ Cpk = \min \left( \frac{56 - 50}{3 \cdot 2}, \frac{50 - 44}{3 \cdot 2} \right) = 1 \]
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
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