The Hit-and-Miss Manufacturing Company produces items that have a probability p
ID: 429831 • Letter: T
Question
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 en- tire 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 qual- ity is determined before the final assembly leaves the plant. Ini- tially 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 nondefec- tive) 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 alternative actions, the states of nature, and the payoff table if the single item is not inspected in advance.
Explanation / Answer
Production Lot=150 Units
Probability for 80 % i.e.120 Units is .05
Probability for 20 % i.e.30 Units is .25
Total Defective units will be = 120*.05+ 30*.25= 13.50 units per Lot
Option I- Screening the item before use at a cost of USD 10 Per Item and replace defective units.
Option II- Use Directly without screening which results in rework cost of USD 100 Per Defective Units.
Initial Inspection Cost = USD 125
Total cost of inspection 13.50*10= 135+125= USD 260
Cost per Unit= 19.26
Cost per unit under option II is 100, hence option I is better to follow.
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