Although traditional acceptance sampling plans (ASPs) need certain mass quality characteristics, it is not easy to define them as crisp value in some real case problems. The fuzzy set theory (FST) is one of the popular techniques to model uncertainties of the process and therefore fuzzy ASPs have been offered in the literature. Fuzzy set extensions have been proposed recently for better modeling of the uncertainties having different sources and characteristics. One of these extensions named neutrosophic sets (NSs) can be used to increase the sensitiveness and flexibility of ASPs. The ASPs based on NSs can give ability to classify the items as defective, non-defective and indeterminate. Since the operator can become indecisive for slightly defective items, these plans can provide a good representation of human evaluations under uncertainty. In this study, single and double ASPs are designed based on NSs by using binomial and poisson distributions that are also re-analyzed based on NSs. For this aim, some characteristics functions of ASPs such as probability of accepting a lot (P-a), average outgoing quality (AOQ), average total inspection (ATI) and average sample number (ASN) have also been analyzed based on NSs. Numerical examples are presented to analyze the proposed plans.