The formula to calculate the Cpk Index (Cpk) is:
\[ Cpk = \min\left(\frac{USL - \mu}{3\sigma}, \frac{\mu - LSL}{3\sigma}\right) \]
Where:
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.
Formula: \( Cp = \frac{USL - LSL}{6\sigma} \)
Example: \( Cp = \frac{10 - 2}{6 \times 0.5} \)
Formula: \( Cpk = \min \left( \frac{USL - \mu}{3\sigma}, \frac{\mu - LSL}{3\sigma} \right) \)
Example: \( Cpk = \min \left( \frac{10 - 6}{3 \times 0.5}, \frac{6 - 2}{3 \times 0.5} \right) \)
Formula: \( Cp = \frac{USL - LSL}{6\sigma} \) and \( Cpk = \min \left( \frac{USL - \mu}{3\sigma}, \frac{\mu - LSL}{3\sigma} \right) \)
Example: \( Cp = \frac{12 - 4}{6 \times 0.6} \) and \( Cpk = \min \left( \frac{12 - 8}{3 \times 0.6}, \frac{8 - 4}{3 \times 0.6} \right) \)
Formula: \( Cpk = \min \left( \frac{USL - \mu}{3\sigma}, \frac{\mu - LSL}{3\sigma} \right) \)
Example: \( Cpk = \min \left( \frac{15 - 10}{3 \times 0.7}, \frac{10 - 5}{3 \times 0.7} \right) \)
