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 (): 0.06 mm
• Overall process mean (): 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:

Step 2: Calculate the Process Performance Index

The formula for is:

Substitute the values:

Interpretation:

• A 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 . 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
• Decrease from the 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.