Pp

374. Pp

374.1. $𝑃_{𝑝}$ (Process Performance Index)

𝑃_{𝑝} = \frac{USL - LSL}{6 𝜎_{overall}}

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

Step 1: Determine the Specification Width

The specification width is the difference between the USL and LSL.

Specification Width = USL - LSL = 10.2 mm - 9.8 mm = 0.4

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

The formula for $𝑃_{𝑝}$ is:

𝑃_{𝑝} = \frac{Specification Width}{6 𝜎_{overall}} = \frac{USL - LSL}{6 𝜎_{overall}}

Substitute the values:

𝑃_{𝑝} = \frac{0.4 mm}{6 \times 0.06 mm} = \frac{0.4 mm}{0.36 mm} = 1.11

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.

374. Pp

374.1. 𝑃𝑝 (Process Performance Index)

374.1. $𝑃_{𝑝}$ (Process Performance Index)