William, a Quality Inspector for Neal Inc., is concerned about the quality of a

Question

William, a Quality Inspector for Neal Inc., is concerned about the quality of a batch of several thousand items that his company will be receiving next week. Neal Inc. manufactures refrigerators for restaurants and is expecting a shipment of evaporators, an important component of the refrigerator. William decides to first conduct a break-even analysis to see which inspection approach might be most appropriate from a cost perspective—no inspection, sampling, or full inspection.
William assumes that the number of defective items in each batch is a random variable. Accordingly, if the cost of replacing a defective evaporator once it has been assembled is $61 and the cost of inspecting items in the incoming shipment is $3 each, below what estimated proportion of defectives in the batch would William prefer to use a sampling methodology instead of 100% inspection?

A. 2.3% defective

B. 4.9% defective

C. 4.7% defective

D. 5.2% defective

Explanation / Answer

The Answer is option B. 4.9% defective

Consider the following Notation:

Let us assume that the population lot has 100 items and 100% of items need to be audited. Hence inspection cost is $300 ($3 * 100)

The Replacement cost is $61 per item. Hence, the Inspection of samples should be below (300/61 = 4.91%). The reason for this samples is because, anything above this % will lead to higher replacement cost and anything below this % will lead to higher inspection cost of 100% testing. Hence, 4.9% or below testing will ensure that the cost will be minimum. Therefore, option B is correct.

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