Probability help

#1
I'm trying to set up a probability analysis to determine if a recall is necessary. We found one of our 13 machines started to break down fairly rapidly. We inspected back to the wharehouse, and on the last 3 units we found they were without defects. 14 out of 29 units had anywhere from 1 to 101 defects. Poisson dist. just doesn't seem to fit the problem which is, what is the probability of an escape from the factory? We have a targeted probability to meet. Any help would be appreciated.