Solve the Loss Function Task-

Nuclear fuel rods are being produced at a plant where the wall thickness has a target thickness of 3.5 mm. The USL for these rod wall thicknesses is 3.8 mm and an LSL of 3.2 mm ( 3.5 plus or minus .3mm) Costs for reject-able parts is $5.50, therefore the parts must be very close to target value. The rockers that produce the rods are 15 years old and produce parts with a mean of 3.5 mm and a standard deviation of 0.3 mm. After the new units are installed the standard deviation is .1 mm. The plant produces 5775 acceptable units per month. Newer rocker units can produce 600 more units per month at a cost of $15,000.00

Determine the Taguchi Loss Function for this example and the time needed to pay back this expenditure. Decide whether this improvement would be beneficial.