Probability problem - Probability of a System Not Working Based on Simulation Result

[harrisWH]

Hi all, I come across a probability question at work and have been struggling to calculate the right probability.

I have a simulation program to simulate a system operating continuously for a day (24 hours * 60 = 1440 minutes), and predict how many minutes the system will "freeze" (the system is not working). The program simulated 150 minutes out of 1440 minutes that the system will freeze.

If in reality, the system would only operates for 100 minutes continuously in a day (can be any continuous 100 minutes in a day), Is that correct to say that the probability of finding one minute in a day that the system freezes is 150/1440 * 100/1440 = 0.723%?
and any though on how I should calculate the probability of finding two minutes in a day that the system freezes?

Thanks!

 

[blamocur]

I am not sure you have enough data to make a reasonable estimate because I cannot see any way to figure out the probability distribution of the events. I have several questions about your post:

1. Do you consider your system to be discrete, i.e. do you look at the state of the system at each minute as a distinct event? For example, what if the system is frozen from 10:20 to 15:37, i.e. 317 seconds?
2. If the system is treated as a distinct set of events, i.e. states at each minute, are those events independent?
3. Do you want to compute the probability that the system is frozen for exactly 1 minute out of 100, or that it is frozen at least 1 minute out of 100?
4. Similar question about finding 2 minutes, but in addition: do you want the probability that the system is frozen for 2 minutes in a row, or do you include the events when the system is frozen two different times for 1 minute each.