The diameter of a forged part has specifications of 120 ± 5mm. A sample of 25 parts chosen from the process gives a sample mean of 122 mm with a sample standard deviation of 2 mm.
(a) Find the Cpk index for the process, and comment on its value. What is the proportion of nonconforming parts assuming normality? If the target value is 120 mm, find the Cpm and Cpmk indices and comment on their values. If the process mean is to be set at the target value, how much of a reduction would occur in the proportion nonconforming?
(b) Parts with a diameter below the lower specification limit cost $ 1.00 per part to be used in another assembly; those with a diameter above the upper specification limit cost $0.50 per part for rework. If the daily production rate is 30,000 parts, what is the daily total cost of nonconformance if the process is maintained at its current setting? If the process mean is set at the target value, what is the daily total cost of nonconformance?