Question: A firm has purchased 30 Mactronics robots, described in Problem. If replaced as a block, the parts cost $20 each, but cost $400 each when replaced after failure.
a. Find the optimal block replacement strategy.
b. Compare this to the cost of replacing the items as they fail.
c. Compare the cost of the block replacement policy you obtained in part (a) with the solution you obtained in part (b). Is the block replacement strategy preferred to an individual replacement strategy?
Problem: Mactronics produces industrial robots. Each robot contains a part with a lifetime of five years at most, and at least one year. Lifetimes between one and five years are equally likely. If the part fails during operation, replacement costs are estimated to be $400, whereas the part can be replaced before failure for $50. When should the part be replaced?
[Hint: The lifetime distribution is uniform on 1, 2, 3, 4, 5-. Assuming discrete variables, this means that f(x) = 1/5 for x = 1, 2, . . . , 5.]