Observations with missing data are a typical predicament in the context of multivariate statistical process control (MSPC). When process control is performed using a $T^2$ control chart of the principal components (PCs), several score imputation methods have been proposed. Some of these lead to estimators with good properties. However, there are no detailed studies pertaining the performance of Phase II Hotelling's $T^2$ and squared prediction error (SPE) charts when such imputation methods are used. In this paper, a simulation study was conducted to assess the consequences of the estimation of incomplete observations using score imputation methods on $T^2$ and SPE control charts. The study involves several scenarios that combine different correlation structures for the PCA model, methods of score estimation, percentages of missing data and patterns of incomplete information. Results show that the charts' standard control limits are adequate only for small percentages of missing values and that their average run lengths (ARLs) tend to be larger than expected in out‐of‐control situations. To illustrate the conclusions of the study, we present two examples. Our findings lead us to suggest a modification that may result in an improvement in the performance of the $T^2$ and SPE control charts.

中文翻译：

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评估缺失值的插补对II期多变量控制图性能的影响

在多元统计过程控制（MSPC）的背景下，缺少数据的观察是典型的困境。当使用${Ť}^{\mathrm{2个}}$在主要成分（PC）的控制图上，已经提出了几种得分插补方法。其中一些导致估计器具有良好的属性。但是，目前尚无关于第二阶段酒店业表现的详细研究。${Ť}^{\mathrm{2个}}$以及使用此类插补方法时的平方预测误差（SPE）图。在本文中，进行了一项模拟研究，以评估使用分数插值方法估算不完整观测值的后果。${Ť}^{\mathrm{2个}}$和SPE控制图。这项研究涉及几种方案，这些方案结合了PCA模型的不同相关结构，得分估算方法，丢失数据的百分比以及不完整信息的模式。结果表明，图表的标准控制极限仅适用于一小部分缺失值，并且在失控情况下其平均行程长度（ARL）往往会比预期的大。为了说明这项研究的结论，我们举两个例子。我们的发现促使我们提出了一种修改方案，可能会导致改进${Ť}^{\mathrm{2个}}$ 和SPE控制图。