Ppk

375. Ppk

375.1. $𝑃_{𝑝 𝑘}$ (Process Performance Index with Centering)

𝑃_{𝑝 𝑘} = Min (\frac{USL - 𝜇_{overall}}{3 𝜎}, \frac{𝜇_{overall} - USL}{3 𝜎})

Example

Suppose a company manufactures metal rods, and the specification limits for the diameter of the rods are:

Upper Specification Limit (USL): 10.2 mm
Lower Specification Limit (LSL): 9.8 mm
Overall standard deviation ( $𝜎_{overall}$ ): 0.06 mm
Overall process mean ( $𝜇_{overall}$ ): 10.1 mm

Step 1: Calculate the Distance from the Process Mean to the Specification Limits

Calculate the distance from the overall process mean to both the USL and LSL:

USL - 𝜇_{overall} = 10.2 mm - 10.1 mm = 0.1 mm

𝜇_{overall} - LSL = 10.1 mm - 9.8 mm = 0.3 mm

Step 2: Calculate the Process Performance Index $𝑃_{𝑘}$

The formula for $𝑃_{𝑝 𝑘}$ is:

𝑃_{𝑝 𝑘} = Min (\frac{USL - 𝜇_{overall}}{3 𝜎}, \frac{𝜇_{overall} - USL}{3 𝜎})

Substitute the values:

𝑃_{𝑝 𝑘} = Min (\frac{0.1 mm}{3 \times 0.06 mm}, \frac{0.3 mm}{3 \times 0.06 mm})

𝑃_{𝑝 𝑘} = Min (\frac{0.1 mm}{0.18 mm}, \frac{0.3 mm}{0.18 mm})

𝑃_{𝑝 𝑘} = min (0.56, 1.67) = 0.56

Interpretation:

A $𝑃_{𝑝}$ of 1.11 indicates that the process performance, considering all sources of variation over time, is capable but less so than the potential capability indicated by $𝐶_{𝑝}$ . The value being slightly above 1 suggests that the process can generally produce rods within specifications, but there might be more variability in the process compared to the short-term capability measured by $𝐶_{𝑝}$
Decrease from the $𝐶_{𝑝}$ value (1.33 to 1.11) reflects the impact of additional variability when evaluating the process over a longer time or under different conditions.

Use:

When you need to evaluate the actual performance of a process over a longer period, considering all sources of variation, including shifts, drifts, and other long-term factors.

375. Ppk

375.1. 𝑃𝑝𝑘 (Process Performance Index with Centering)

375.1. $𝑃_{𝑝 𝑘}$ (Process Performance Index with Centering)