The impact of metrology study sample size on uncertainty in IAEA safeguards calculations

Abstract

Abstract. Quantitative conclusions by the International Atomic Energy Agency (IAEA) regarding States' nuclear material inventories and flows are provided in the form of material balance evaluations (MBEs). MBEs use facility estimates of the material unaccounted for together with verification data to monitor for possible nuclear material diversion. Verification data consist of paired measurements (usually operators' declarations and inspectors' verification results) that are analysed one-item-at-a-time to detect significant differences. Also, to check for patterns, an overall difference of the operator-inspector values using a "D (difference) statistic" is used. The estimated DP and false alarm probability (FAP) depend on the assumed measurement error model and its random and systematic error variances, which are estimated using data from previous inspections (which are used for metrology studies to characterize measurement error variance components). Therefore, the sample sizes in both the previous and current inspections will impact the estimated DP and FAP, as is illustrated by simulated numerical examples. The examples include application of a new expression for the variance of the D statistic assuming the measurement error model is multiplicative and new application of both random and systematic error variances in one-item-at-a-time testing.

Comprehensive Uncertainty Quantification in Nuclear Safeguards

“…Recent options for top-down UQ, such as constrained estimators or Bayesian estimators that use prior information, offer possible improvements over existing variance component estimators. Any such improvements in estimated RSDs should be accompanied by uncertainties in the RSDs, which means that uncertainty in the estimated uncertainties matters [2,7]. The ABC approach in Section 3 appears to provide a robust estimate of the posterior distribution of the RSDs.…”

“…Many different sequential statistical tests were evaluated. In a related context, [2] evaluated the impact of uncertainty in measurement error RSDs on estimated DPs in verification data. …”

“…NDA measurements often have larger uncertainty at larger true values, which implies a multiplicative rather than an additive error model. However, provided that the individual RSDs are fairly small, resulting in a total RSD of approximately 10% or less, a multiplicative error model such as = (1 + + ) can be analyzed in the same manner as an additive error model, by analyzing on the log scale [1,2]. Therefore, for brevity, only an additive error model such as in (8) .…”

“…In international safeguards, the inspector randomly selects items to verify NM declarations made by the operator. The difference statistic, = ∑ =1 (( − )/ ), defined as the average difference in the sample of size n (extrapolated to the population of size N) between operator declarations (almost always based on operator measurements) and inspector measurements can be used as a test statistic, or the statistic [2] can be used to compute the inspector MB statistic (or sequence). Inspector MB = MB − , which could be analyzed using sequential statistical methods such as those in Section 4.3.…”

“…In NMA, one MB or a collection of MBs are tested for the presence of any statistically significant large differences and/or for trends, while allowing for random and systematic errors in variance propagation to estimate the measurement error standard deviation of MB , MB . Similarly, in verification activities done by an inspector, paired operator and inspector data are tested for any large differences and/or for trends [1,2]. Therefore, both material balance evaluation and verification activities require statistical analyses, which require UQ.…”