To make sure the products are up to standards, we have two types of sampling to

Question

To make sure the products are up to standards, we have two types of sampling to inspect

The third option is ‘no inspection’- which is carried out when the inspection costs are too high compared to repairing defects

Which one to choose:

Decision choose one among the options is usually based on costs and the measure used is

Breakeven point, BEP = cost of inspection per item / cost of later repair due to a defective item

Let P = estimated proportion of defectives in the lot.

Decision

P BEP ,use acceptance sampling

P > BEP, use 100% inspection

P < BEP and P is variable, use acceptance sampling

P < BEP and P is stable, no inspection

For the above problem,

Cost of inspection per item =$ 0.80

Cost of later repair due to a defective item =$20

BEP = 0.80/20 =0.04

P = estimated proportion of defectives in the lot =5/100=0.05

0.05 > 0 .04

P > BEP, therefore 100 percent inspection is justified assuming percentage defective is stable.

However, if the percentage defective is variable, then acceptance sampling should be used

Explanation / Answer

5. A process for manufacturing shock absorbers for light trucks produces 5% defectives. Inspection cost per shock is $0.80, and 100% inspection generally catches all defects. Any defectives shock absorbers installed on trucks must eventually be replaced at a cost of $20 per shock. Is 100% inspection justified?

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