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

Question

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

Quizplus · Accepted Answer

If the standard deviation decreases, the process spread decreases. As a result, the process becomes more precise, which increases the process capability index (Cpk). Therefore, the process capability index (Cpk) of the process will always increase if the standard deviation (σ) of the process decreases, assuming other things remain constant.

Other Things Remaining the Same, and Assuming Thatis Smaller Than