Determining sampling plans in acceptance sampling to reduce producer and consumer risks

Abstract

In this paper, we find the best sampling plan in acceptance sampling, to reduce producer and consumer risks. A sampling plan consists of two parameters, the sample size and the maximum allowed number of defectives. For a given sample size, there is a trade-off between the producer risk and the consumer risk. Which risk would be higher would depend on the other parameter which decides the sampling plan, the maximum allowed number of defectives. We show that as the sample size is increased, both producer and consumer risks can be reduced together. But increasing the sample size, means additional inspection cost for each and every sample. So, risk reduction would happen at a cost. Typically, the binomial distribution is used to determine the producer and consumer risks for a sampling plan. In the model, we use the normal approximation to the binomial. With the model, the sampling plan can be found very quickly, using Excel.