I am trying out my luck with the first post here...
Well, to start off I have a problem, and I am not really sure about the solution. I hope that someone might chime in with suggestions..
We have an ionizing radiation detector. It is sampling the radiation induced counts each second. The counts in the detector are Poisson distributed. Then, a source might pass the detector giving rise to the number of counts in the detector for some time. We want to have a threshold for counts in the detector, which when passed would indicate that there is a source nearby. The question is whether we are correctly estimating the threshold for a certain detection criteria set for a given number of false alarms.
For example, given, that the total survey time is one hour there are 3600 individual measurements in total. We want to set the threshold of detection to 1 false alarm per hour or 1 in every 3600 measurements. Due to the fact, that the counts in the detector are Poisson distributed around the mean of $\lambda_\text{bkg}$, we can estimate the threshold level $N_\text{alarm}$ using Poisson CDF for a probability of $P_\text{alarm}=1-\frac{1}{3600}$. To do that, I am using qpois(lambda,p) function in R. As far as I understand it should yield correct alarm level.
Testing the results using a number of simulated one-hour measurements yields average probability of any number of alarms of around 25% for a given one-hour survey. For a number of alarms greater than one, the probability is around 3%.
Is this correct? Or maybe I missing something?