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Certain types of food products, such as dried fruits and nuts, are presented for inspection in lots of one or two hundred to several thousand boxes or bags, each box or bag containing a large number of individual items. The quality of a lot is measured by the proportion of defective items contained in the aggregate, but the labor cost of locating, opening, and sampling a box or bag is generally many times that of inspecting an individual item, dictating inspection of the maximum possible number of items from the minimum number of boxes. The distribution of defectives between boxes may however be nonuniform, so that the frequency distribution of the number of defectives occurring in a fixed number of items from randomly chosen boxes is not binomial. In some such instances, the distribution may be satisfactorily representable by a negative hypergeometric frequency function which allows a greater variance than would the binomial. A minimum-cost two-stage single sampling plan for the classification of good and bad quality lots, with specified risks of error calculated from this distribution, is described, boxes or bags constituting the primary sampling units and individual items the secondary sampling units.
Dunnett, C. W.
Statistician, Food and Drug Divisions, Ottawa,
Hopkins, J. W.
Biometrician, Division of Applied Biology, National Research Council, Ottawa,