Minimum cost acceptance sampling plans for grain control, with application to GMO detection

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 controle 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.