Design of Fuzzy Sampling Plan Using the Birnbaum-Saunders Distribution

Acceptance sampling is one of the essential areas of quality control. In a conventional environment, probability theory is used to study acceptance sampling plans. In some situations, it is not possible to apply conventional techniques due to vagueness in the values emerging from the complexities of processor measurement methods. There are two types of acceptance sampling plans: attribute and variable. One of the important elements in attribute acceptance sampling is the proportion of defective items. In some situations, this proportion is not a precise value, but vague. In this case, it is suitable to apply flexible techniques to study the fuzzy proportion. Fuzzy set theory is used to investigate such concepts. It is observed there is no research available to apply Birnbaum-Saunders distribution in fuzzy acceptance sampling. In this article, it is assumed that the proportion of defective items is fuzzy and follows the Birnbaum-Saunders distribution. A single acceptance sampling plan, based on binomial distribution, is used to design the fuzzy operating characteristic (FOC) curve. Results are illustrated with examples. One real-life example is also presented in the article. The results show the behavior of curves with different combinations of parameters of Birnbaum-Saunders distribution. The novelty of this study is to use the probability distribution function of Birnbaum-Saunders distribution as a proportion of defective items and find the acceptance probability in a fuzzy environment. This is an application of Birnbaum-Saunders distribution in fuzzy acceptance sampling.