Bayesian Updating of Material Balances Covariance Matrices Using Training Data

Abstract

The main quantitative measure of nuclear safeguards effectiveness is nuclear material accounting (NMA), which consists of sequences of measured material balances that should be close to zero if there is no loss of special nuclear material such as Pu. NMA is essentially “accounting with measurement errors,” which arise from good, but imperfect, measurements. The covariance matrix MB of a sequence of material balances is the key quantity that determines the probability to detect loss. There is a recent push to include process monitoring (PM) data along with material balances from NMA in new schemes to monitor for material loss. PM data includes near-real-time measurements by the operator to monitor and control process operations. One concern regarding PM data is the need to estimate normal behavior of PM residuals, which requires a training period prior to ongoing testing for material loss. Assuming that a training period is used for PM data prior to its use in statistical testing for loss, that same training period could also be used for improving the estimate of MB that is used in NMA. We consider updating MB using training data with a Bayesian approach. A simulation study assesses the improvement gained with larger amounts of training data.