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"If the failure rate is really 1 in 10^6, the probability of selling a defective part is also 1 in 10^6.
(Assuming failure and defective mean the same thing.)
If inspection catches 80% of the defective parts (4 out of 5), then the probability of selling a defective parts goes up to 1 in 5x10^6.
If you sell (and continue to sell) 100K parts per year, you can expect to sell one defective part every 50 years. "
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Or the testing may cost more than the replacement.
doing no QA you still have a low rate of sold failures. As soon as (sic. asuming "assuming that") a failure doesn't harm someones life it sure is easier to handle this via insurance or refunds than doing any QA at all
If you manufacture 5,000,000 parts
4,999,995 are good
5 are defective
4,999,995 x 0.8 of the good parts pass ==> 3,999,996 to sell
but 5 x 0.2 of the bad parts do too ==> 1 gets sold
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