Neutron multiplicity counting (NMC) measurements are often affected by the detection system dead time. Still, dead time losses are often neglected in analytic NMC models, and most of the dead time corrections are done through empirical models, experimentally fitted to the measurement system. In the present paper, we introduce a new analytic model for calculating the effect of a system dead time on the outcome of NMC. The model is subjected to two assumptions (in addition to the standard model assumptions in multiplicity counting): The first is that the dead time can be described by a paralyzable model, and the second is that the dead time effect may occur only between neutrons arriving from the same source event. The second assumption is, in fact, a restriction on the source event rate in the system and, in certain cases, may eventually be translated into a restriction on the mass of the measured sample.