The upper specification limit USL of a bottlefilling process

The upper specification limit (USL) of a bottle-filling process is set to 12 ounces, and underfilling (the lower specification limit [LSL]) is not viewed as an important problem. Which of the following is true of this process?

A. Such a process is always capable, regardless of its mean and standard deviation.

B. For the purpose of computing the capability index, one can assume that LSL = USL.

C. Such a process is never capable because the capability index cannot be calculated.

D. For the purpose of computing the capability index, one can assume that LSL = 0.

Solution

Process Capability index ( Cpk) is calculated as :

Cpk = Minimum ( ( USL – mean)/ 3 x standard deviation , ( Mean – LSL) / 3 x standard deviation )

Process Capability index is thus very much dependent on the process mean and standard deviation. It is also true that one cannot comment about the process capability without calculating the capability index

Following statements are therefore not true :

c)Such a process is never capable because capability index cannot be calculated

Also when LSL = USL = 12 , it means only ounce needs to be filled. Th problem statement however states that “Underfilling is not viewed as an important problem”. Therefore following statement is also not true :

The correct statement therefore is “D. For the purpose of computing capability index, one can assume that LSL = 0 “

Answer : d) for the purpose of computing capability index , one can assume that lsl = 0