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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?

Christian
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  • Perhaps you have managed to find the actual minimum and maximum with the experiments. Or perhaps getting lower than your simulated minimum or higher than your simulated maximum are so unlikely that you do not come across them. Or perhaps your experiments are exploring the wrong combinations of inputs to cover all the possibilities. We cannot tell, but one approach might be to see which inputs tend to lead to lower occupancy and which higher, and then try experiments which aim to get new record lows or record highs in a less random way. – Henry Dec 04 '20 at 12:36
  • @Henry yes, those are the options I'm dealing with. I thought I could infer something from how far are the events "a new maximum (or minimum) has been found". So in the first 20 realisations I could expect this to happen quite often, but what if I perform 500 tests and this a new maximum/minimum has not been found in the last 300 realisations? Couldnt I infer anything from the first 200 realisations and from the frequency of this event? I am afraid that the stimulus inputs are too many to try to finely search, but I will bear that in mind. – Christian Dec 04 '20 at 12:58

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