I completed my Engineering Mathematics degree 7 years ago so my Stats is a bit rusty. I'm working on a real-world issue at work and wanted to apply some probability to learn the likelihood of some events happening (or not). I'll be generic but its regarding the performance on a Phase Lock Loop (PLL) on some telecommunications hardware we are thinking of procuring.
The Phase Lock Loop issue is ultimately misbehaving which results in a brief loss of our electrical signal that I am trying to carry over a "System" at input. At the far end of the "System" the signal also can experience the same type of misbehavior at output but independently of the input - So, basically an issue at input or output could happen independently of one another. Essentially I would like to understand the likelihood of a misbehavior at either independent port over any given time period.
I have empirical data that tells me the number of incidences I have had to date (and this continues to add to my data set as we continue to monitor lab devices long-term) - i.e. Number of misbehavior in a give number of hours...
I think a Poisson distribution would suit an event happening in a given time frame but how could I understand the probability of either a Input misbehavior or Output misbehavior happening in the "System"?
If there are any samples of this I can learn from (genuinely interested in refreshing my skills) that would be great or if someone wants to help spell this out for me I'm sure I can taking the learning this way...
Thanks.
If input errors occur at a rate of $r_i$ per hour and output errors occur at a rate of $r_o$ per hour, then the expected number of errors in a time period of length $t$ is $\lambda = (r_i+r_o) t$. Assuming a Poisson model, the probability of no error (either input or output) in that time period is $e^{-\lambda}$.
One of the best sources for information on this type of model is Introduction to Probability Models by Sheldon Ross.