A bottling machine fills water bottles with an average of 12.000 ounces of water. The standard deviation is 0.002 ounces. If the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces, calculate the process capability index of the machine.
A) Less than or equal to 1
B) More than 1 but less than or equal to 2
C) More than 2 but less than or equal to 3
D) More than 4

Question

Quizplus · Accepted Answer

The process capability index (Cpk) is calculated as the minimum of (USL - mean)/(3*standard deviation) and (mean - LSL)/(3*standard deviation). Here, USL = 12.015, LSL = 11.985, mean = 12.000, and standard deviation = 0.002. Cpk = min((12.015-12.000)/(3*0.002), (12.000-11.985)/(3*0.002)) = min(2.5, 2.5) = 2.5, which is more than 2 but less than or equal to 3.

A Bottling Machine Fills Water Bottles with an Average of 12.000