Sample Sizes for Attributes Inspection When Strata are Heterogeneous

The formula that is in common usage at the International Atomic Energy Agency (IAEA) when calculating sample sizes for inspection by attributes is based on the assumption that the stratum in question is homogeneous with respect to element/isotope weight, i.e., all items in the stratum have the same weight. In practice, this assumption is generally invalid to some extent. This paper examines the effect of heterogeneity in item weights on the probability of detection, and indicates how sample sizes might be altered to account for the heterogeneity. After considering the simplest type of heterogeneity that occurs when the item weights cluster tightly about a small number of modal points, a more general pattern of heterogeneity is examined. Modifications to the sample sizes to account for this general pattern are derived based on a specific diversion strategy. A number of numerical results are presented in the form of plots relating sample size to mean item weight and to the scatter in item weights.