Could you please suggest me a distribution or stochastic process which would fit the following problem?
I have a device under test, and there is a buffer within it, of which I would like to find out the maximum and minimum fill level occupancy when exercised under different stimulus inputs. In each test realisation, the stimulus inputs are randomised (infinite combinations), leading potentially to a different minimum and/or maximum occupancy than that observed in the previous tests. What is the probability that after performing N realisation tests, I will not observe any variation in the minimum and maximum occupancy in the tests performed afterwards regardless of how many are performed (the maximum fill level resulting from these tests performed afterwards is equal or smaller than that obtained during the first N tests, and similarly for the minimum)? Is there any known stochastic process or any popular experiment in statistics I could start to look at?