Modified acceptance sampling for statistical quality control

In the article, we look into a situation where a company receives from a producer a shipment consisting of product lots. The products within the lot should be of an established quality; nevertheless, the consumer has to make sure that they are. In order to check the quality of the product lot, a sample of items is selected therefrom, and a certain quality characteristic is measured. Depending on the measurement results, the lot is either accepted or rejected. The aim is to find a minimal sample size balancing the risks of the producer and those of the consumer at certain predefined levels. Usually, the homogeneity of the lot is assumed, and an equal probability one or more phases sampling design is used for acceptance sampling. However, in some cases, the lots are not homogeneous: the items may be of different size, weight or other properties. In the article, some unequal probability sampling designs are proposed for acceptance sampling. Based on the established value of the admissible proportion of defective items as a prior parameter, the posterior distribution for the proportion is constructed, and a Bayesian hypothesis about the lot acceptance is tested. The sample size is determined by simulation from the posterior, taking into account the risks of the producer and those of the consumer. The method can be extended to other sampling designs for which a posterior distribution of the proportion of defective items can be constructed.