Sample-based regulatory intervention for managing risk within heterogeneous populations, with phytosanitary inspection of mixed consignments as a case study

Inspection of consignments of imported goods is commonly undertaken at national borders in order to prevent incursions of pests and diseases and deter malefactors. Inspection of the whole consignment is usually either impossible or inefficient, so inspection of a random sample is used instead.\n\nThe size of the random sample for plant products is justified by appeal to International Standards for Phytosanitary Measures No. 31, \"Methodologies for Sampling of Consignments\". ISPM 31 notes that \"A lot to be sampled should be a number of units of a single commodity identifiable by its homogeneity [...]\" and \"Treating multiple commodities as a single lot for convenience may mean that statistical inferences can not be drawn from the results of the sampling.\"\n\nHowever, commonly consignments are heterogeneous, either because the same commodities have multiple sources or because there are several different commodities. The ISPM 31 prescription creates a substantial impost on border inspection because it suggests that heterogeneous populations must be split into homogeneous sub-populations from which separate samples of nominal size must be taken.\n\nWe demonstrate that if consignments with known heterogeneity are treated as stratified populations and the random sample of units is allocated proportionally based on the number of units in each stratum, then the nominal sensitivity at the consignment level is achieved if our concern is the level of contamination in the entire consignment taken as a whole. We argue that unknown heterogeneity is no impediment to appropriate statistical inference. We conclude that the international standard is unnecessarily restrictive.