In this note, we revisit the $g$ and $h$ control charts that are commonly used for monitoring the number of adverse cases between the nonconformities. It is known that the process parameter of these charts is usually unknown and estimated by using the maximum likelihood estimator and the minimum variance unbiased estimator. However, the minimum variance unbiased estimator in the control charts has been inappropriately used in the quality engineering literature. This observation motivates us to provide the correct minimum variance unbiased estimator and investigate theoretical and empirical biases of these estimators under consideration. Given that these charts are developed based on the underlying assumption that samples from the process should be balanced, which is often not satisfied in many practical applications, we propose a method for constructing these charts with unbalanced samples.

翻译：在本说明中,我们重新审视了通常用于监测不一致情况之间不利情况数量的g美元和h美元控制图表,已知这些图表的流程参数通常未知,并且使用最大可能性估计器和最小差异不偏差估计器来估计这些图表的流程参数,然而,在质量工程文献中,控制图表中的最低差异不偏差估计器使用不当。这一观察促使我们提供正确的最低差异不偏差估计器,并调查审议中的这些估算器的理论和经验偏差。鉴于这些图表是根据以下基本假设编制的,即该流程的样本应当平衡,而在许多实际应用中往往不能满足这一假设,我们提出了用不平衡的样本构建这些图表的方法。