Improved estimation of the variance in Monte Carlo criticality calculations

Results for the effective multiplication factor in a Monte Carlo criticality calculations are often obtained from averages over a number of cycles or batches after convergence of the fission source distribution to the fundamental mode. Then the standard deviation of the effective multiplication factor is also obtained from the keff results over these cycles. As the number of cycles will be rather small, the estimate of the variance or standard deviation in keff will not be very reliable, certainly not for the first few cycles after source convergence. In this paper the statistics for keff are based on the generation of new fission neutron weights during each history in a cycle. It is shown that this gives much more reliable results for the standard deviation even after a small number of cycles. Also attention is paid to the variance of the variance (VoV) and the standard deviation of the standard deviation. A derivation is given how to obtain an unbiased estimate for the VoV, even for a small number of samples. (authors)