We consider the problem of estimating the rate of defects (mean number of defects per item), given the counts of defects detected by two independent imperfect inspectors on one sample of items. In contrast with the setting for the well-known method of Capture–Recapture, we do not have information regarding the number of defects jointly detected by both inspectors. We solve this problem by constructing two types of estimators—a simple moment-type estimator, and a complicated maximum-likelihood (ML) estimator. The performance of these estimators is studied analytically and by means of simulations. It is shown that the ML estimator is superior to the moment-type estimator. A systematic comparison with the Capture–Recapture method is also made.

中文翻译：

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估计不完善抽样检验下的缺陷率——一种新方法

我们考虑估计缺陷率（每个项目的平均缺陷数）的问题，给定两个独立的不完美检查员在一个项目样本上检测到的缺陷计数。与众所周知的 Capture-Recapture 方法的设置相比，我们没有关于两个检查员共同检测到的缺陷数量的信息。我们通过构建两种类型的估计器来解决这个问题——一个简单的矩型估计器，一个复杂的最大似然 (ML) 估计器。这些估计器的性能是通过分析和模拟来研究的。结果表明，ML 估计器优于矩型估计器。还与 Capture-Recapture 方法进行了系统比较。