I have a process made up of, on average, about 10 independant subprocesses that follow approximately a normal distribution. I know the individual distributions of the subprocesses, but not the distribution of the overall process made up of the subprocesses.
I would like to select the mean value + 3*sigma of the overall process, i.e mean(overall_process) + 3*sigma(overall_process).
Or, more specifically : I have to find a way to sample the individual subprocesses whose distributions are known in such a way that by doing so would be the same as sampling the distrubution of the overall process at mean(overall_distribution) + 3*sigma(overall_distribution).
What constraints must I apply when I sample the individual subprocesses in order to achieve this goal ?
(What I was doing up to now was to sample the individual subprocesses at mean(subprocess) + 3*sigma(subprocess) but of course this is not correct because the value I get is much much larger than the mean+3*sigma of the overall process)
Any help much appreciated