Other things remaining the same, and assuming that is smaller than USL and larger than LSL, if the standard deviation (σ) of the process decreases, process capability index (Cpk) of the process will
A)Stay the same
B)Will always increase.
C)Will always decrease
D)Either B or C
E)Will sometimes increase

Question

Quizplus · Accepted Answer

Cpk is a measure of how well the process meets the specifications. It considers the distance between the process mean and the specification limits, as well as the variability within the process. 
If the standard deviation of the process decreases, then the process becomes more consistent and the distance between the mean and the specification limits decreases. As a result, the Cpk value will increase, indicating an improvement in the process capability. Therefore, the correct answer is B, the Cpk will always increase when the standard deviation decreases.

Other Things Remaining the Same, and Assuming That Is Smaller