The Hit-and-Miss Manufacturing Company produces items that have a probabilitypof being defective. These items are produced in lots of 150. Past experience indicates thatpfor an entire lot is either 0.05 or 0.25. Furthermore, in 80 percent of the lots produced,pequals 0.05 (sopequals 0.25 in 20 percent of the lots). These items are then used in an assembly and ultimately their quality is determined before the finally 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.

1. Develop a decision analysis formulation of this problem if the single item is not inspected in advance. Obtain an optimal policy for this model.

2. 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.

3. Develop a decision analysis formulation of this problem if the single item is can be inspected in advance. Obtain an optimal policy for this model.

4. Determine EVSI and EVPI. Is inspecting the single item worthwhile?