STATISTICAL METHODS FOR EVALUATING SEQUENTIAL MATERIAL BALANCE DATA

Present material balance accounting methods focus primarily upon the "material unaccounted for" (MUF) statistic, which utilizes the data from only one material balance period as an indicator of a possible loss of nuclear material. Typically a cumulative MUF (CUMUF) statistic, which utilizes all the available flow data, is also calculated; but there is no statutory requirement that it be reported or evaluated. Previous work has shown that cumulative MUF has greater power than MUF to detect small constant losses. Techniques which emphasize the sequential nature of MUF (that is, MUF as a sequence of values related over time) are also expected to be more sensitive for detecting losses. The recursive estimation algorithm known as the Kalman filter has been proposed as a possible solution which uses the above idea. The purpose of this study was to evaluate the application of the Kalman filter to the MUF problem, to propose other approaches to the problem, and to re-examine the traditional MUF and cumulative MUF statistics in more general settings. The report considers the material balance model where the only modeled variability is that due to the measurements of the net throughput (inputs minus outputs) and the inventories. The problem discussed is how to extract more information from all the available data. Material balance models which assume no loss, and the constant loss and all-at-once loss situations are considered. Emphasis was placed on explaining state variable models and Kalman filtering in relation to the general linear statistical model to which least squares is applied yielding a minimum variance unbiased estimator. All errors affecting material balances were assumed to be random