Statistical evaluation of two triggering systems: an application of conditional variance

Previous results related to measurement variances in neutron coincidence counting (NCC) indicate a disagreement between theory and experiment. In NCC, each detected neutron opens two coincidence gates and counts the number of neutrons that arrive within the allotted time period of the first neutron. Similarly, previous results for studying the alarm rate of a broadband radio-frequency collection system (to detect the radio-frequency emitted from nuclear explosions or lightning for example) are shown to lead to poor approximations for some parameter ranges. In a typical example of this type of system, the master trigger could alarm if five or more of eight sub-bands alarm within a specified time window beginning from an alarm from one or more sub-bands. cribe a simple but powerful statistical result involving conditional variance that corrects the previous results in both applications, and we demonstrate the adequacy of the results using real and simulated NCC data and simulated broadband radio-frequency data.