The Hit-and-Miss Manufacturing Company produces items that have a probability p of being defective. These items are produced in lots of 150. Past experience indicates that p for an entire lot is either 0.05 or 0.25. Furthermore, in 80 percent of the lots produced, p equals 0.05 (so p equals 0.25 in 20 percent of the lots). These items are then used in an assembly, and ultimately their quality is determined before the final assembly leaves the plant. Initially the company can either screen each item in a lot at a cost of $10 per item and replace defective items or use the items directly without screening. If the latter action is chosen, the cost of rework is ultimately $100 per defective item. Because screening requires scheduling of inspectors and equipment, the decision to screen or not screen must be made 2 days before the screening is to take place. However, one item can be taken from the lot and sent to a laboratory for inspection, and its quality (defective or nondefective) can be reported before the screen/no screen decision must be made. The cost of this initial inspection is $125.
(a) Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table if the single item is not inspected in advance.
(b) Assuming the single item is not inspected in advance, use Bayes’ decision rule to determine which decision alternative should be chosen.
(c) Find EVPI. Does this answer indicate that consideration should be given to inspecting the single item in advance?
(d) Assume now that the single item is inspected in advance. Find the posterior probabilities of the respective states of nature for each of the two possible outcomes of this inspection.
(e) Find EVE. Is inspecting the single item worthwhile?
(f) Determine the optimal policy.