• • 上一篇    

高维稳健Hotelling $T^2$控制图的研究与应用

姜云卢, 丰之韵   

  1. 暨南大学经济学院, 广州 510632
  • 收稿日期:2021-12-11 修回日期:2022-03-16 发布日期:2022-08-31
  • 基金资助:
    国家自然科学基金项目(12171203)和广东省自然科学基金项目(2019A1515011830,2022A1515010045)资助课题.

姜云卢, 丰之韵. 高维稳健Hotelling $T^2$控制图的研究与应用[J]. 系统科学与数学, 2022, 42(7): 1877-1890.

JIANG Yunlu, FENG Zhiyun. Research and Application of High-Dimensional Robust Hotelling $T^2$ Control Chart[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(7): 1877-1890.

Research and Application of High-Dimensional Robust Hotelling $T^2$ Control Chart

JIANG Yunlu, FENG Zhiyun   

  1. School of Economics, Jinan University, Guangzhou 510632
  • Received:2021-12-11 Revised:2022-03-16 Published:2022-08-31
控制图是统计过程控制中最广泛使用的技术之一,主要通过检测异常或失控的行为监控生产质量.传统Hotelling$T^2$控制图具有不稳健性,对存在异常值数据的监控效果不够理想.虽然基于MCD估计的稳健Hotelling$T^2$控制图能够更好地抵抗异常值的影响,但是MCD估计的精度会随着维数的增加而降低,在维数大于样本量的情形下,不仅$T^2$统计量无法计算,MCD估计方法也会失效.因此本文提出基于MRCD估计的高维稳健Hotelling$T^2$控制图,以实现对产生高维数据过程的有效监控.模拟实验和实证分析的结果表明,基于MRCD估计的高维稳健Hotelling$T^2$控制图的监控效果更优,能够很好地抵抗异常值的影响,极为有效地对过程中的异常情况发出警报.
Control charts are one of the most widely used techniques in statistical process control to monitor production quality by detecting abnormal or out-of-control conditions. However, the traditional Hotelling $T^2$ control chart is not robust, which results in unsatisfactory effect when monitoring data with outliers. Although the robust Hotelling $T^2$ control chart based on MCD estimation can better resist the influence of outliers, the accuracy of MCD estimation decreases with the increase of dimension. Particularly, when the dimension is larger than the sample size, Hotelling $T^2$ statistics cannot be calculated, which leads to the failure of MCD estimation method. Therefore, this paper proposes a high-dimensional robust Hotelling $T^2$ control chart based on MRCD estimation to effectively monitor the process with high-dimensional data. Our simulation and empirical analysis results show that the high-dimensional robust Hotelling $T^2$ control chart based on MRCD estimation has better monitoring effect, that is, it can not only resist the influence of outliers well, but also effectively warn the abnormal situation in the process.

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