A decision about quality

Probability Level 1

A toothbrush factory produces 200,000 toothbrushes every day. The manufacturing process isn't perfect, and there are sometimes toothbrushes made with defects.

An analyst has calculated that each toothbrush has a 0.004 probability of having a defect. If a customer receives a defective product, then it will cost the company $5 to replace the product and satisfy the customer.

The factory manager can choose to hire a Quality Assurance team to find and fix all defective toothbrushes as they are produced. What is the maximum amount the factory manager would be willing to spend on this team per day?

$4,000 $5,000 $800 $10,000

1 solution

Andy Hayes
Jun 13, 2016

If the factory produces 200,000 toothbrushes per day, and each toothbrush has a 0.004 probability of being defective, then we can estimate that the factory produces $200000\times 0.004=800$ defective toothbrushes per day.

Each of these defective toothbrushes costs the company $5, so the total cost for defects per day is $\$5\times 800=\$4000$ .

If the QA team can catch all defects, then it stands to reason that the cost of the QA team should be less than the cost of the defects. Therefore, the manager would spend up to $4000 per day on the QA team.

Andy Hayes,as a fresher to learn probability thanks for making my views clear.

Subbu Saravanan - 3 years, 4 months ago

Here is the difference between QC(Quality Control) and QA(Quality Assurance)

Shubhrajit Sadhukhan - 7 months, 1 week ago

I take issue with that. Why would a manager higher QA staff without realizing any benefit, cost-savings? If total cost is the exactly the same, why go through the bother of hiring additional staff? QA staff will not have a 100% efficiency/accuracy. Some defective product will still make it to the consumer. Which means the manager should target a daily chost of less than $4000, not equal to it.

Tony Campos - 4 years, 6 months ago

Yes, in a real-world situation, a QA team wouldn't be able to catch all defects. It's given in the assumptions of this problem that this particular QA team catches all defects. It's also stated in my solution that the $4000 is the most that the manager would be willing to spend. I am going to edit the problem to make this more clear.

This problem isn't intended to be super-realistic. It's just meant to get readers to start thinking about how probability is used in the real-world. Real-world problems require many more assumptions and adjustments, and even then, a good manager would want to frequently audit costs and benefits to see if his/her decisions are having the intended effect.

Andy Hayes - 4 years, 6 months ago

One thing I would like to add...... The manager is willing to spend $4,000 on inspection team. Better to reduce faulty products then losing their reputation while the faulty product goes into the hands of the customers......

Ramajigalu M Puneeth - 3 years, 8 months ago

corporate_reputation++

Maksims Strašinskis - 2 years, 8 months ago

A decision about quality

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