XYZ manufacturing has received an order to produce a rod 5 inches in diameter + .04 inch. In sample runs, the machine tool that will be making the rod has been able to produce rods with a mean diameter of 4.99 inches and a standard deviation of 0.011 inch. The process capability index for this process is
A) 0.91
B) 1.51
C) -0.91
D) -1.51

Question

XYZ manufacturing has received an order to produce a rod 5 inches in diameter + .04 inch. In sample runs, the machine tool that will be making the rod has been able to produce rods with a mean diameter of 4.99 inches and a standard deviation of 0.011 inch. The process capability index for this process is
A) 0.91
B) 1.51
C) -0.91 
D) -1.51

Quizplus · Accepted Answer

To determine the process capability index, we use the following formula:
Cp = (upper specification limit - lower specification limit) / (6 x standard deviation)
In this case, the upper specification limit is 5.04 inches (5 + 0.04) and the lower specification limit is 4.96 inches (5 - 0.04). Substituting these values and the given standard deviation into the formula, we get:
Cp = (5.04 - 4.96) / (6 x 0.011) = 0.727
Since the process is centered around the target value (4.99 inches), we can also calculate the process capability index using the following formula:
Cpk = min[(upper specification limit - mean) / (3 x standard deviation), (mean - lower specification limit) / (3 x standard deviation)]
Substituting the given values, we get:
Cpk = min[(5.04 - 4.99) / (3 x 0.011), (4.99 - 4.96) / (3 x 0.011)] = min[1.36, 0.91] = 0.91
Therefore, the process capability index for this process is 0.91, which is closest to choice A.

XYZ Manufacturing Has Received an Order to Produce a Rod