I tested an older software and I found one fault per 10 hours run/10 times run. New version of the software has created. How can I prove the software is operating correctly. How many test should I run? I used Poisson-distribution with 0.01 significance level for that and my solution is the following(1 fault per 10 hours):
1 − e^(−0.1*x) = 0.99 x = ~46 hours.
No matter how much testing you do, you can never PROVE the bug has been fixed.
But if we assume that the number of appearances of the bug per time period has a Poisson distribution with a mean of $\lambda = 0.1$ per hour, then the probability of observing zero bugs in a run of length $t$ hours is $\exp (-0.1 \;t)$. So, for example, if there is no change then the probability that you run for $46$ hours and do not observe the bug is $\exp(-0.1 \times 46) \approx 0.01$.