One of the most widely used multivariate control charts is the Hotelling T². In order to construct a Hotelling T² control chart, the mean vector (μ) and the variance–covariance matrix (Σ) must be first estimated. The classical estimators of μ and Σ are usually used to design Hotelling T² control chart. The classical estimators are sensitive to the presence of outliers. One way to deal with outliers is to use robust estimators. In this study, a robust T² control chart is proposed. The mean vector is obtained from the sample median. The median absolute deviation and the comedian are used as the estimates of the elements of the variance–covariance matrix. The proposed robust estimators of the mean vector and the variance–covariance matrix are compared with the sample mean vector and the sample variance–covariance matrix, and the M estimator of these parameters, through efficiency and robustness measures. The performances of the proposed robust T² control chart and the classical and the M estimators are also compared by means of average run length. Simulation results reveal that the proposed robust T² control chart has much better performance than the traditional Hotelling T² and similar performance to the M estimator in detecting shifts in process mean vector. Use of other robust estimators to estimate the process parameters is an area for further research.

中文翻译：

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使用基于中位数的估计量的稳健T2控制图

最广泛使用的多元控制图之一是Hotelling T ²。为了构造一个Hotelling T ²控制图，必须首先估计平均矢量（μ）和方差-协方差矩阵（Σ）。μ和Σ的经典估计量通常用于设计Hotelling T ²控制图。古典估计量对异常值的存在很敏感。处理离群值的一种方法是使用健壮的估计量。在这项研究中，稳健的T ²提出了控制图。从样本中位数获得平均向量。中位数绝对偏差和喜剧演员用作方差-协方差矩阵元素的估计。通过效率和鲁棒性测度，将提出的均值向量和方差-协方差矩阵的鲁棒估计量与样本均值向量和样本方差-协方差矩阵以及这些参数的M估计量进行比较。还通过平均游程长度比较了建议的鲁棒T ²控制图和经典估计量与M估计量的性能。仿真结果表明，所提出的鲁棒T ²控制图具有比传统Hotelling T ²更好的性能。在检测过程均值向量的偏移方面与M估计器的性能相似。使用其他鲁棒估计器估计过程参数是需要进一步研究的领域。