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how to calculate this probability problem?
i have a device that has a probability of failure when operated, acceptable failure rate is lets say 1%
now i have to test if the device conforms to this criteria or not
up to lets say 2% of the devices i test may later be found to be non-conforming, no more
i can test for its functionality but the probability for finding the problem with single test is the same 1% failure rate. fortunately i can perform the test n times.
So the question is, how many times do i have to perform the test to be 98% sure the device conforms to max 1% failure rate criteria
1 Answer
- MorewoodLv 71 decade agoFavorite Answer
I'm not sure I have understood your conditions:
A device can be conforming or non-conforming.
You test the device, if it fails you discard it.
If it passes there is a 1% chance that it is non-conforming, hence a 99% chance that it is conforming. So if a given device passes one test, there is a 99% chance (greater than 98%) that it is conforming.
If you perform the test n times, and the tests are independent, the the chance of a non-conforming device passing all n times is (1%)ⁿ = 1/100ⁿ. So, after n tests, you have a certainty of 1-1/100ⁿ that the device is conforming. After 1 test, 99%. After 2 tests, 99.99%. After 3 tests, 99.9999%. etc.