Well that's a loaded question. First, you can't "prove" anything (perhaps you can change your degree of confidence in your conclusions). Second, how do you know the failure rate is .05ppm? How do you know your test is "good" (measurement error)? Do you know if the process is consistent?
You could take either a probabilistic approach or an analytical approach to building your confidence in the low failure rate. I usually don't care much about whether the rate is "correct" or not. I am usually applying statistical method to discover what factors affect the rate.
"All models are wrong, some are useful" G.E.P. Box
