Which of the following pairs correctly identifies the changes to the percentage of defective parts and the process capability index?

A supplier making a part with a specified dimension of 50 mm + 0.3 mm changes the tolerance range to + 0.5 mm.

Which of the following pairs correctly identifies the changes to the percentage of defective parts and the process capability index?
A . The percentage of defective parts increases, and the process capability index increases.
B . The percentage of defective parts increases, and the process capability index decreases.
C . The percentage of defective parts decreases, and the process capability index increases.
D . The percentage of defective parts decreases, and the process capability index decreases.

Answer: D

Explanation:

The percentage of defective parts is the proportion of units that do not meet the specification limits. The process capability index (Cpk) is a measure of how well the process can produce within the specification limits. Both the percentage of defective parts and the Cpk depend on the specification

range and the process variation1.

If the supplier changes the tolerance range from + 0.3 mm to + 0.5 mm, the specification range becomes wider, which means that more units will fall within the specification limits and fewer units will be defective. Therefore, the percentage of defective parts decreases.

However, if the process variation remains unchanged, the Cpk will decrease, because Cpk is inversely proportional to the specification range2. A wider specification range means a lower Cpk, which indicates a lower process capability. A lower Cpk also implies a higher percentage of defective parts in relation to the process variation3.

Therefore, the correct answer is D. The percentage of defective parts decreases, and the process

capability index decreases.

Reference: Understanding Process Capability Index (Cpk) [With Calculator] [Process Capability Index – an overview | ScienceDirect Topics] Converting A Capability Index to PPM Defective – Accendo Reliability