The issue of food safety in modern life has become a worldwide concern, especially since edible oil is essential for the human body and many types of food processing. To control the raw material quality adequately, an incoming quality control plan is very critical. Further, the consumer should have an appropriate acceptance sampling plan to evaluate the outgoing quality of oil products. When 100% inspection is not possible, a good acceptance sampling plan utilizing random samples with reasonable size can protect the producer and consumer. The information extracted from samples can be used to estimate the product's quality. In this paper, the process capability index C_(pu)^T is used to deal with the problem of product acceptance determination for a product with multiple independent characteristics. An illustration example based on peanut oil with specifications of benzopyrene and various polycyclic aromatic hydrocarbon (PAHs) is presented.