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An Improvement of the Hotelling T~2 Statistic in Monitoring Multivariate Quality Characteristics

机译：监测多元质量特征的Hotelling T〜2统计量的改进

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摘要

The Hotelling T~2 statistic is the most popular statistic used in multivariate control charts to monitor multiple qualities. However, this statistic is easily affected by the existence of more than one outlier in the data set. To rectify this problem, robust control charts, which are based on the minimum volume ellipsoid and the minimum covariance determinant, have been proposed. Most researchers assess the performance of multivariate control charts based on the number of signals without paying much attention to whether those signals are really outliers. With due respect, we propose to evaluate control charts not only based on the number of detected outliers but also with respect to their correct positions. In this paper, an Upper Control Limit based on the median and the median absolute deviation is also proposed. The results of this study signify that the proposed Upper Control Limit improves the detection of correct outliers but that it suffers from a swamping effect when the positions of outliers are not taken into consideration. Finally, a robust control chart based on the diagnostic robust generalised potential procedure is introduced to remedy this drawback.
机译：Hotelling T〜2统计量是多变量控制图中用于监视多个质量的最流行的统计量。但是，该统计数据容易受到数据集中存在多个异常值的影响。为了纠正这个问题，已经提出了基于最小体积椭球和最小协方差决定因素的鲁棒控制图。大多数研究人员根据信号的数量评估多元控制图的性能，而没有过多关注那些信号是否真的离群值。在适当考虑的情况下，我们建议不仅根据检测到的异常值评估控制图，还要根据其正确位置进行评估。本文还提出了基于中位数和中位数绝对偏差的控制上限。这项研究的结果表明，拟议的“控制上限”可改善对正确异常值的检测，但是如果不考虑异常值的位置，则会受到沼泽化的影响。最后，引入了基于诊断鲁棒性广义潜在过程的鲁棒性控制图来弥补这一缺陷。

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  • 来源
    《Mathematical Problems in Engineering》 |2012年第5期|p.50.1-50.15|共15页
  • 作者

    Ashkan Shabbak; Habshah Midi;

  • 作者单位

    Statistical Research and Training Center (SRTC), 1433873487 Tehran, Iran,Laboratory of Computational Statistics and Operation Research, Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Malaysia;

    Laboratory of Computational Statistics and Operation Research, Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Malaysia,Mathematics Department, Faculty of Science, University Putra Malaysia, 43400 Serdang, Malaysia;

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