For a key joint, a precision machining process has a lower specification limit of a width of 0.99 mm and an upper specification limit of 1.01 mm. The standard deviation is 0.005 mm and the mean is 1 mm.
a. What is the process capability index for the bottle filling process?
b. The company now wants to reduce its defect probability and operate a “six sigma process.”
To what level would they have to reduce the standard deviation in the process to meet this target?