Beyond Probability: An Analytical Exploration of Fuzzy and Neutrosophic Paradigms in Binomial Acceptance Sampling

Acceptance sampling plans are widely used in Statistical Quality Control to determine the acceptance or rejection of production lots based on sample inspection. Classical sampling plans under the binomial distribution assume precise parameter values, which may not adequately represent uncertainty, vagueness, and indeterminacy encountered in practical inspection environments. This review summarizes acceptance probability formulations for single and double sampling plans developed using fuzzy and neutrosophic logic under the binomial distribution. The focus is on studies that model the fraction defective and related parameters as fuzzy or neutrosophic numbers, allowing imprecise and indeterminate quality information to be incorporated into sampling decisions. The reviewed approaches demonstrate greater flexibility than classical methods and highlight the role of neutrosophic logic in explicitly accounting for indeterminacy in acceptance decision-making. This paper serves as a concise reference for researchers working on uncertainty-based acceptance sampling in manufacturing and quality control applications.