I work in Aerospace Engineering. Aerospace components are often subjected to cyclic loads and can fail in "fatigue". The designers design the parts against fatigue failures using the "fatigue life" of the materials, typically obtained by testing the coupons under cyclic loads. The fatigue life is defined as the number of cycles to failure when subjected to a specific applied cyclic load level. 

However, there can be a lot of scatter in the data. Therefore, to be conservative, the designer uses the "minimum fatigue capability" of the materials, which is typically the "1/1000", or the "-3 sigma" value. I would like to figure out the minimum number of coupons one needs to test to obtain either the 1/1000 value, or the "-3 sigma" value. Your help or suggestion for further readings would be much appreciated.

To me, the 1/1000 means one has to ensure that only 1 in 1000 parts has fatigue life less than or equal to the 1/1000 value, but I am lost as to how to obtain that value. 

In my mind, to obtain the -3 sigma fatigue life, one could test, say, 10 coupons, calculate the mean value and the standard deviations. Then subtract 3 standard deviations from the mean value to obtain the -3 sigma value. However, one could do the same with 5 coupons or 20 coupons, but the -3 sigma value would be very different. So the question is, how does one determine the appropriate sample size to produce a representative (statistically significantly?) -3 sigma value? I think it depends on the type of distribution, and I would like to assume a normal distribution to keep things simple for now.