A manufacturer is considering replacement of an existing machine that performs an operation on a part. The variable costs are $0.38 per piece on the existing machine and $0.05 per piece on the new machine. The cost of the new machine is $40,000, while the existing machine can be scrapped at a value of $5400. It is known that the proportion nonconforming using the existing machine is 0.05. With the new machine, since the nonconformance rate will be influenced by the operator and the new machine, it cannot be specified exactly. Based on experience, the estimated probability distribution of the proportion nonconforming for the new machine is shown in Table 10-10. An order exists for 100,000 parts. Assume that the entire cost of the new machine can be assigned to this order. Note that costs may have to be calculated on the basis of good parts produced.
(a) If a decision has to be made without sampling, what is that decision? What is the expected opportunity loss of the optimal decision?
(b) Suppose that the seller of the new machine gives you the opportunity to sample the output from a new machine set up at another plant. You select a sample of 100 parts and find 4 nonconforming. What is your optimal decision?
Proportion Nonconforming, p Probability, P(p)
0.05 ........................................................... 0.20
0.07 ........................................................... 0.25
0.09 ........................................................... 0.35
0.11 ........................................................... 0.30