Improved method of estimating the product quality after multiple inspections
针对多次检验中缺陷检测概率不恒定的实际情况，提出beta-几何检验模型，用beta分布描述检测概率的异质性，数值实验表明该模型优于传统常数概率方法。
A complex product is often inspected more than once in a sequential manner to ensure the product’s quality. Based on the number of defects discovered during each round of inspection process, we can estimate the number of defects still remaining in the product. For each defect, the probability that the defect will be detected during each inspection cycle is usually assumed to be a known ‘constant’. However, in many practical situations, some defects are easily detected, while others are much more difficult to identify. In this paper, we propose a ‘beta-geometric’ inspection model in which the heterogeneity in detection probability is described by a beta distribution. In a numerical study, we show that our more realistic inspection model clearly outperforms traditional estimation methods that are based on the assumption of a constant detection probability.