Solve previous problem 20.25, except that the average value of the dimension produced by process B is 0.10 mm greater than the nominal value specified. The average value of the dimension produced by process A remains at the nominal value N.
Problem 20.25
Two alternative manufacturing processes, A and B, can be used to produce a certain dimension on one of the parts in an assembled product. Both processes can produce parts with an average dimension at the desired nominal value. The tolerance on the dimension is ( 0.15 mm. The output of each process follows a normal distribution. However, the standard deviations are different. For process A, ( = 0.12 mm; and for process B, ( = 0.07 mm. Production costs per piece for A and B are $7.00 and $12.00, respectively. If inspection and sortation is required, the cost is $0.50 per piece. If a part is found to be defective, it must be scrapped at a cost = its production cost. The Taguchi loss function for this component is given by L(x) = 2500(x - N)2, where x = value of the dimension and N is its nominal value. Determine the average cost per piece for the two processes.