Variance results for the second and third reduced sample moments in neutron multiplicity counting for randomly triggered or signal-triggered counting gates

Neutron multiplicity counting is an established method to estimate the spontaneous fission rate, and therefore also the plutonium mass for example, in a sample that includes other neutron sources. The extent to which the sample and detector obey the “point model” assumptions impacts the estimate's total measurement error, but, in nearly all cases, for the random error contribution, it is useful to evaluate the variances of the second and third reduced sample moments of the neutron source strength. Therefore, this paper derives exact expressions for the variances and covariances of the second and third reduced sample moments for either randomly triggered or signal-triggered non-overlapping counting gates, and compares them to the corresponding variances in simulated data. Approximate expressions are also provided for the case of overlapping counting gates. These variances and covariances are useful in figure of merit calculations to predict assay performance prior to data collection. In addition, whenever real data are available, a bootstrap method is presented as an alternate but effective way to estimate these variances.