The approach commonly used to find the variance of material unaccounted for (MUF) involves expressing MUF as a linear combination of beginning and ending inventories, plant inputs, and plant outputs. The variance is found for each of these components, and the variance of MUF is then found by appropriately combining the component variances. Covariances that may exist between the various quantities are often ignored or, at best, only partially accounted for.
A modification of this approach is suggested. This modification directs attention away from finding the variances separately for the inputs, outputs, and inventories, and is motivated by the need to more easily recognize the covariance sources, and properly account for them.
The MUF is, of course, simply an algebraic sum of individual terms. The same is true of other quantities of interest to safeguards, such as total inventory of a given type material. Thus, the results in this paper may be applied to any algebraic sum which satisfies the assumptions on model structure, even though attention is focused on calculating the variance of MUF.
In this paper, it is assumed that the basic safeguards measurements consist of net weights, element factors (uranium or plutonium), and isotopic factors. In this treatment, the use of non-destructive assay measurements, (e.g., on solid wastes), is not covered explicitly, but their inclusion is not difficult. Further, although presented with reference to a fuel fabrication facility, the results are readily applicable to other types of facilities as well.