Effects of Neutrosophic Binomial Distribution on Double Acceptance Sampling Plans

Abstract

Acceptance sampling plans (ASPs) offers to inspect a small set instead of all outputs in a production process. This approach minimizes the inspection cost dramatically and guarantees the output quality within a predefined risk ratio based on a small sample size. One type of ASPs named double acceptance sampling plans (DASPs) gives an ability to minimize the effect of the randomness on inspection results and reach a lower risk level with a small sample size. We know that the ASPs use certain values while formulation and application procedures. However, it is also clear that quality characteristics may not be certain in some real cases and they include some vagueness. So, we need some new techniques to model the uncertainty and manage human’s evaluations. The fuzzy set theory (FST) is one of the most popular techniques to model the uncertainty in the engineering problems. Additionally, we know that the fuzzy extensions such as Neutrosophic sets (NSs) bring some advantages to manage these uncertainties. Generally, fuzzy DASPs is offered in the literature but it is formulated with α-cut approach to convert the problem into interval valued set problem. With the help of this conversion, it is enough to solve the problem with certain values for the upper and the lower limits of the intervals. However, the uncertainty is generally more complex in real life applications including human factor. NSs that include three terms, truthness (t), indeterminacy (i) and falsity (f) and cover inconsistent data cases are good representation of human thinking under uncertainty. In this study, DASPs are formulated and analyzed based on NSs by using binomial distribution. A numerical example is also presented to analyze the proposed sampling plans based on NSs.

Keywords

• Acceptance double sampling plans
• Binomial distribution
• Fuzzy sets
• Neutrosophic sets

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