VPSim: Variance propagation by simulation

One of the fundamental concepts in a materials control and accountability system for nuclear safeguards is the materials balance (MB). All transfers into and out of a material balance area are measured, as are the beginning and ending inventories. The resulting MB measures the material loss, MB = T{sub in} + I{sub B} {minus} T{sub out} {minus} I{sub E}. To interpret the MB, the authors must estimate its measurement error standard deviation, {sigma}{sub MB}. When feasible, they use a method usually known as propagation of variance (POV) to estimate {sigma}{sub MB}. The application of POV for estimating the measurement error variance of an MB is straightforward but tedious. By applying POV to individual measurement error standard deviations they can estimate {sigma}{sub MB} (or more generally, they can estimate the variance-covariance matrix, {Sigma}, of a sequence of MBs). This report describes a new computer program (VPSim) that uses simulation to estimate the {Sigma} matrix of a sequence of MBs. Given the proper input data, VPSim calculates the MB and {sigma}{sub MB}, or calculates a sequence of n MBs and the associated n-by-n covariance matrix, {Sigma}. The covariance matrix, {Sigma}, contains the variance of each MB in the diagonal entries and the covariance between pairs of MBs in the off-diagonal entries