A Note on the Variance of the Estimated Nuclear Material Content in Batches Sampled via Composite Techniques

For nuclear material accounting purposes, it may be necessary to determine the variance of the estimated quantity of nuclear material in a set of batches of product where each batch consists of multiple containers. Frequently, each container will be sampled and the samples will be composited for subsequent chemical analysis. When replicate samples are obtained from each container and separately composited, the differences between the replicate composite sample measurement results are often used to estimate the variance due to the combined sources of sampling and measurement error. This paper will demonstrate that, for highly non-homogenous materials, this method may underestimate the total variance due to sampling error sources. Furthermore, the paper proposes a method for quantifying the variance of the estimated nuclear material content in sets of batches sampled via composite techniques based on data obtained from a designed sampling study. An example is provided that is based on measurement results obtained from batches of uranium-bearing material at the BWXT Nuclear Operations Group, Inc. Lynchburg facility.