Verification of the history-score moment equations for weight-window variance reduction

The history-score moment equations that describe the moments of a Monte Carlo score distribution have been extended to weight-window variance reduction. The resulting equations have been solved deterministically to calculate the population variance of the Monte Carlo score distribution for a single tally. Results for oneand two-dimensional one-group problems are presented that predict the population variances to less than 1% deviation from the Monte Carlo for one-dimensional problems and between 1–2% for two-dimensional problems.