Minimum cost acceptance sampling plans for grain control, with application to GMO detection A. Kobilinsky a, * , Y. Bertheau b a INRA, Biome ´trie (BIA), Domaine de Vilvert, 78352 Jouy-en Josas Cedex, France b INRA, PMDV/MDO, RD 10, Route de Saint-Cyr. 78026 Versailles Cedex, France Received 13 October 2003; received in revised form 29 June 2004; accepted 7 July 2004 Available online 19 September 2004 Abstract Quality control by attribute [A. Hald, Statistical Theory of Sampling Inspection by Attributes, Academic Press, New York, 1981; E.G. Schilling, Acceptance sampling in quality control. In: Statistics: Textbooks and Monographs, Vol. 42, Dekker, 1982; J.J. Daudin, C.S. Tapiero. Les outils et le contro ˆ le de la qualite ´. Economica (1996).] may be used with grain lots to control their purity. But usually the control cannot be made on each grain separately. The presence of an impurity is rather assayed in groups of grains the size of which is an important parameter which can be used to find a cost optimal acceptance sampling plan among those which give acceptable consumer’s and producer’s risks. This group control has been studied for virus or bacterium detection in grains by the Elisa method [Y. Maury, C. Duby, J.M. Bossenec, G. Boudazin, Group analysis using ELISA: determination of the level of transmission of Soybean Mosaic Virus in soybean seed, Agronomie 5, 1985, 405–415; Y. Maury, C. Duby, R.K. Khetarpal, Seed certification for viruses. In: Plant Virus, Disease Control, A. Hadidi, R.K. Khetarpal, H. Koganezawa, eds., APS Press, Chap. 18, 1998, 237–248.] and is advocated by Remund et al. [K. Remund, D. Dixon, D. Wright, L. Holden, Statistical considerations in seed purity testing for transgenic traits, Seed Sci. Res. 11, 2001, 101–119.] for genetically modified organism (GMO) detection. But no optimization method to select the cheapest acceptance single- or double-sampling plan has yet been described. Given a control cost function depending on the number of groups to analyse and on the total number of grains, we describe in this paper a practical way to get the least expensive acceptance sampling plan keeping both the consumer’s and the producer’s risks below a predetermined threshold. The method is more specially illustrated by examples in GMO detection. D 2004 Elsevier B.V. All rights reserved. Keywords: Seed acceptance sampling; Quality control; Operating characteristic curve; Single sampling by attributes; double sampling by attributes; Group analysis; GMO detection 1. Introduction In grain production and commercialisation, the purity and absence of defect of a grain lot processed has to be checked for various criteria. For instance, its ability to germinate, its belonging to the indicated variety, its good health state, the absence of toxics like mycotoxin, etc. Recent advances in agricultural biotechnology have produced new transgenic varieties whose characteristics have to be thoroughly studied before they can be authorized for commercialisation. Hence, there is also an important need to control that no such unauthorized genetically modified organism (GMO) exists in the commercialised lots of grains, or when legislation makes the labelling compulsory that it has been adequately labelled. In some case, the analysed criteria can be evaluated by a quantitative response. For instance, the optical density in an ELISA method, the cycle threshold (Ct) in a real time polymerase chain reaction (RtPCR), etc. can be calibrated to predict microorganism or GMO concentration. But doing that rigorously implies a good knowledge of the distribution of the response and its uncertainty. 0169-7439/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.chemolab.2004.07.005 * Corresponding author. Tel.: +33 1 34 65 22 30; fax: +33 1 34 65 22 17. E-mail address: kobi@jouy.inra.fr (A. Kobilinsky). Chemometrics and Intelligent Laboratory Systems 75 (2005) 189 – 200 www.elsevier.com/locate/chemolab