The specifications for the thickness of nonferrous washers are 1.0±0.04 mm. From process data, the distribution of the washer thickness is estimated to be normal with a mean of 0.98 mm and a standard deviation of 0.02 mm. The unit cost of rework is $0.10, and the unit cost of scrap is $0.15. For a daily production of 10,000 items:
(a) What proportion of the washers is conforming? What is the expected total daily cost of rework and scrap?
(b) In its study of constant improvement, the manufacturer changes the mean setting of the machine to 1.0 mm. If the standard deviation is the same as before, what is the expected total daily cost of rework and scrap?
(c) The manufacturer is trying to improve the process and reduces its standard deviation to 0.015 mm. If the process mean is maintained at 1.0 mm, what is the percent decrease in the expected total daily cost of rework and scrap compared to that of part (a)?