Thank you.
Real world application: this is example from my plant inspection.
OK, so you are most interested in the worst case failure rate. Now, it does depend upon what level of significance you want - 90% is usually the lowest accepted, but 95% is very common, also 99%.
If you wanted to go upper 90% single sided, then the formula would be .11 + 1.28 x sqrt( .11 x (1-.11)/100). You would be 90% sure that the failure rate is less than that number for the population sampled, with the following assumptions:
1. Your sample was random, each part had an equally likely chance of being chosen.
2. Failures are independent from part to part
3. The failure rate is uniform throughout the population.