Comparison of an Exact to an Approximate Sample Size Calculation for Attribute Testing

To calculate the number of inspector samples to verify declared operator items, the performance measure used by the International Atomic Energy Agency (IAEA) is the probability of finding at least one defective item when the number of defects is at least enough to acquire a significant quantity of nuclear material. The IAEA formula that defines the sample size nIAEA is based on approximating the exact formula for the probability to select one or more defects among the nIAEA samples. One task that emerged from the IAEAs reviewing and updating activities of its statistical methodologies was to evaluate the accuracy of nIAEA. Therefore, this paper shows that an alternative sample size calculation that is based on the exact formula for the non-selection probability leads to a value nIAEA within the set {nIAEA 3,nIAEA 2,nIAEA 1,nIAEA} for all safeguards-relevant cases. The new sample size calculation is slightly more complicated to calculate, but it should not present significant implementation issues; and, in situations where samples are expensive it is appealing, because it requires the same or less inspector samples than nIAEA derived by the IAEA formula.