Multi-stratum Detection Probability Calculations For IAEA Safeguards: Foundations And Early Progress

IAEA safeguards experts use detection probability (DP) as the primary effectiveness metric for nuclear material inventory and flow verification activities. Most commonly, the DP is defined as the probability of identifying at least one defective item in a population, assuming that one significant quantity (SQ) of material has been diverted. The DP is calculated over a spectrum of diversion scenarios (from a few items with gross defects to a large number of items with bias defects), and the worst-case (lowest) DP is reported. Traditionally, safeguards verification activities are performed on the basis of stratified inventories or flows, whereby the material is grouped into strata on the basis of similar physical and chemical characteristics. On the basis of the measurement tools available to verify the material in the stratum, a separate sampling plan is established for each stratum with the aim of achieving a defined DP of detecting the diversion of 1 SQ from the stratum. However, at facilities, sites, and sectors in which multi-stratum diversion scenarios are plausible, it is desirable to calculate the worst-case DP for scenarios in which 1 SQ is diverted from among the various strata. This paper shows that the multi-stratum DP problem can have multiple local minima, so a global constrained-optimization algorithm is appropriate. The solution is estimated by discretizing the amount of material diverted from each stratum. The discretized problem is solved using a brute force approach and a dynamic programming approach. The two approaches calculate similar answers, but dynamic programming is faster for problems with many strata. This work provided background and early approaches that Annadevula et al. have refined and expanded upon in their concurrent publication. Future work is planned to improve the trade-off between discretization error and calculation time.