## Question 822:

Jeff... the previous answer was not quite the answer I was anticipating- let me restate the problem more clearly.
1. A manufacturer has a process which in a given period of performance can produce 176-264 devices.
...a few failures are expected.
2. These devices either pass or fail. Approx p=.95 (1 out of 20 can show a problem or defect)
3. A process reliability of .995 is desired with a 90% confidence level.
What is thethe minimum sample size.

4. I caculated that a cumulative binomial of 176 processed devices with 3 failures and .95= p yields a .993 cum binomial reliability (close enough) .. I believe that is the caculation for a process reliability but I'm not sure how to assess the sample size impact in assigning a 90% confidence level to the .993 reliability caculation.... does this loosen up the sample size by X, ~2.5 std dev? (3sd~99.7CI)
5. It was suggested to change the confidence level to a tolerance interval, possibly use an equivalent form of the normal approximation. So if s= [np(1-p)]^1/2 (binomial std dev) do I calculate a ~2.5sigma 90% CI , i.e. subtract the ~2.5std dev from 176 sample size to get a lower sample size 176-8=168. Can you envision how to apply this. Can you recommend the ways to approach this?

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