A mathematical model is derived for the factorial moments of the probability distribution of neutron signal multiplets within signal-triggered inspection intervals, detected with a paralyzing neutron dead-time counter. These moments are a function of the spontaneous fission rate, the (α ,n) reaction rate, the probability that a neutron generates an induced fission, the neutron detection probability, the dead time, and the nuclear physics data. Monte Carlo calculations are used to check the derived algorithms and the iterative procedure. This procedure is then applied to real measurement data of a PuO2 sample to obtain the correlated multiplets from the numerical values of the factorial moments.