A visualizing method for trade-off between risk and cost when applying acceptance sampling by attributes
Qi Li, Lixian Yang, Fei He, Jun Yu · 2025
Acceptance sampling is the process of inspecting a portion of products in a lot or batch to decide whether to accept or reject the entire lot or batch by means of statistical methods. According to the data properties, it can be divided into acceptance sampling by attributes and by variables. The former is widely applied in engineering practice due to its simplicity and easy acquisition of data. To formulate such kind of sampling plans, it is necessary to determine the input parameters, including acceptance quality limit (AQL), rejectable quality limit (RQL) and two types of risk \(\alpha\) and \(\beta\), thus to determine sample size. However, in reality, we often need to have a trade-off between risk and cost, which means it is not able to determine \(\alpha\) and \(\beta\) risk unless sample size has been considered in conjunction. This paper provides a solution to the problem. After studying the relationship between relevant parameters and sample size under binomial distribution, we introduce a visualizing method using the probability of acceptance - sample size curve and further explain its application. Some practice has shown that the method proposed in this paper can significantly improve the efficiency of developing or analyzing acceptance sampling plans.