A fastener company produces a certain type of bolt for the automobile industry with a nominal (target)length of 2.00 inches.The specifications for the length of the bolt are 2.00 ± .006 inches.An automobile manufacturer will only purchase from this company if the sigma level of capability of the process is at least 4.If the process mean is equal to 2.001,determine the maximum process standard deviation necessary for the fastener manufacturing company in order to qualify as a supplier for the automobile manufacturing company.
A).0125
B).005
C).00125
D).00025

Question

Quizplus · Accepted Answer

To calculate the maximum process standard deviation necessary, we need to first calculate the process capability (CP) and then use it to calculate the process standard deviation (sigma).

Process Capability (CP) can be calculated as:
CP = (Upper Specification Limit - Lower Specification Limit) / (6 * Standard Deviation)

Given that:
Nominal Length (Target) = 2.00 inches
Specification Limit = 2.00 ± 0.006 inches
Mean = Process Mean = 2.001 inches
Sigma = Standard Deviation (to be calculated)

Upper Specification Limit = 2.006 inches
Lower Specification Limit = 1.994 inches

CP = (2.006 - 1.994) / (6 * sigma) = 0.012 / sigma

We know that the automobile manufacturer will only purchase from this company if the sigma level of capability of the process is at least 4. Therefore, we need to set CP = 4 and solve for sigma.

4 = 0.012 / sigma

sigma = 0.012 / 4 = 0.003 = 0.00125 (rounded to nearest 0.00001)

Therefore, the maximum process standard deviation necessary for the fastener manufacturing company is 0.00125 inches. The correct choice is C).

A Fastener Company Produces a Certain Type of Bolt for the Automobile