Process Capability (Cp & Cpk) Calculator
Interactively calculate process capability indices Cp and Cpk with this professional-grade tool, ensuring operational excellence.
Process Inputs
Cpk (min distance to spec)
How to Use This Calculator
Enter your observed process mean, standard deviation, and the upper and lower specification limits. Use the Calculate button or wait for auto-refresh (inputs are debounced) to see Cp and Cpk values that signal whether your process variation fits inside the tolerance window.
Results show the minimum capability (Cpk) as a highlighted score plus the individual Cp value and mean offset so you can judge whether you need faster variation reduction or recentering.
Methodology
The widget uses the classic process capability equations: Cp compares the specification width to six sigma while Cpk takes the tighter of the distance between the mean and each limit, divided by three sigma. The mean offset row reports how far the process center is from the midpoint, measured in sigma units.
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. Questo rapporto storico illustra come derivare Cp e Cpk da limiti di specifica e deviazione standard per migliorare la qualità dei processi.
Glossary of Variables
- Mean (μ): The observed process average around which samples cluster.
- Standard Deviation (σ): A statistical measure of spread used to estimate variation per sample.
- USL: Upper Specification Limit defining the highest acceptable value.
- LSL: Lower Specification Limit defining the lowest acceptable value.
Step-by-Step Example
Suppose a process has μ = 50, σ = 2, USL = 56 and LSL = 44. The capability numbers follow the formulas below.
\[ Cp = \frac{56 - 44}{6 \cdot 2} = 1.00 \]
\[ Cpk = \min \left( \frac{56 - 50}{3 \cdot 2}, \frac{50 - 44}{3 \cdot 2} \right) = 1.00 \]
Because the process is perfectly centered, Cp and Cpk match. The mean offset reads 0σ, so you can focus on reducing variation for even tighter results.
Frequently Asked Questions (FAQ)
What is the Cp index?
Cp quantifies a process's potential capability to stay within USL and LSL assuming perfect centering.
What is the Cpk index?
Cpk reflects the actual capability by accounting for the current mean location relative to the specs.
How do I interpret Cp and Cpk values?
Values above 1.0 generally indicate a capable process, while values below 1.0 signal that variation or offset breaches the tolerance width.
Why is Cpk important?
Cpk considers both variation and mean shift, offering a more accurate picture than Cp when the process is not centered.
Can Cp be greater than Cpk?
Yes—Cp ignores centering, so it can be higher than the more conservative Cpk if the process mean drifts toward one of the specs.
Full original guide (expanded)
The original audit spine highlighted the extracted formulas, LaTeX renditions, and a note to verify that the calculator engine matches the published methodology. All extracted formulas (Cp & Cpk with their sample calculations) remain centrally visible, and the verification checklist encourages comparing ranges, variables, and units before trusting the outputs.