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Abstract : Among the basic concepts in the theory of sampling inspection the producer's and the consumer's risks are the most widely used for characterizing system of sampling plans. It seems therefore strange that a comprehensive theory based on these concepts does not exist. The purpose of the present paper is to present such a theory for the case of single sampling by attributes. The theory naturally covers some wellknown results, but old as well as new results are derived by a common method and compared within the same model. The requirements defining a system of sampling plans are usually of such a nature that no explicit solution exists for the sample size and the acceptance number. The author supplements the exact (implicit) solutions by asymptotic solutions which give a better insight into the basic properties of the systems.
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