Cpk Index Calculator

Formula

The formula to calculate the Cpk Index (Cpk) is:

\[ Cpk = \min\left(\frac{USL - \mu}{3\sigma}, \frac{\mu - LSL}{3\sigma}\right) \]

Where:

Cpk – The process capability index.
USL – The upper specification limit.
μ – The process mean.
σ – The process standard deviation.
LSL – The lower specification limit.

Definition

Cpk Index (Cpk): A statistical tool used in quality control to measure a process’s ability to produce output within specified limits.
Upper Specification Limit (USL): The maximum acceptable value in the specification.
Process Mean (μ): The average value of the process.
Process Standard Deviation (σ): The measure of variability in the process.
Lower Specification Limit (LSL): The minimum acceptable value in the specification.

Example

Let's say the upper specification limit (USL) is 10, the process mean (μ) is 7, the process standard deviation (σ) is 1, and the lower specification limit (LSL) is 4. Using the formula:

\[ Cpk = \min\left(\frac{10 - 7}{3 \times 1}, \frac{7 - 4}{3 \times 1}\right) = \min\left(\frac{3}{3}, \frac{3}{3}\right) = 1 \]

So, the Cpk Index is 1.