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Optimal Food Safety Sampling Under a Budget Constraint
Author(s) -
Powell Mark R.
Publication year - 2014
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/risa.12054
Subject(s) - sample (material) , statistics , sampling (signal processing) , budget constraint , unit (ring theory) , constraint (computer aided design) , acceptance sampling , fraction (chemistry) , sample size determination , mathematics , total cost , operations management , operations research , computer science , engineering , economics , accounting , chemistry , mathematics education , neoclassical economics , geometry , filter (signal processing) , chromatography , organic chemistry , computer vision
Much of the literature regarding food safety sampling plans implicitly assumes that all lots entering commerce are tested. In practice, however, only a fraction of lots may be tested due to a budget constraint. In such a case, there is a tradeoff between the number of lots tested and the number of samples per lot. To illustrate this tradeoff, a simple model is presented in which the optimal number of samples per lot depends on the prevalence of sample units that do not conform to microbiological specifications and the relative costs of sampling a lot and of drawing and testing a sample unit from a lot. The assumed objective is to maximize the number of nonconforming lots that are rejected subject to a food safety sampling budget constraint. If the ratio of the cost per lot to the cost per sample unit is substantial, the optimal number of samples per lot increases as prevalence decreases. However, if the ratio of the cost per lot to the cost per sample unit is sufficiently small, the optimal number of samples per lot reduces to one (i.e., simple random sampling), regardless of prevalence. In practice, the cost per sample unit may be large relative to the cost per lot due to the expense of laboratory testing and other factors. Designing effective compliance assurance measures depends on economic, legal, and other factors in addition to microbiology and statistics.