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A distribution‐free control chart for monitoring high‐dimensional processes based on interpoint distances

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  • Lianjie Shu
  • Jinyu Fan

Abstract

With rapid advances in sensing technology and data acquisition systems, high‐dimensional data appear in many settings. The high dimensionality presents a new challenge to the traditional tools in multivariate statistical process control, due to the “curse of dimensionality.” Various tests for mean vectors in high dimensional situations have been discussed recently; however, they have been rarely adapted to process monitoring. This paper develops a distribution‐free control chart based on interpoint distances for monitoring mean vectors in high‐dimensional settings. Other than the Euclidean distance, the family of Minkowski distance is used for discussion, which is a generalization of the former and other distances. The proposed approach is very general as it represents a class of distribution‐free control charts based on distances. Numerical results show that the proposed control chart is efficient in detecting mean shifts in both symmetric and heavy‐tailed distributions.

Suggested Citation

  • Lianjie Shu & Jinyu Fan, 2018. "A distribution‐free control chart for monitoring high‐dimensional processes based on interpoint distances," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(4), pages 317-330, June.
    • Handle: RePEc:wly:navres:v:65:y:2018:i:4:p:317-330
    DOI: 10.1002/nav.21809
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    References listed on IDEAS

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    1. Graham, M.A. & Chakraborti, S. & Human, S.W., 2011. "A nonparametric exponentially weighted moving average signed-rank chart for monitoring location," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2490-2503, August.
    2. Shuai Huang & Zhenyu Kong & Wenzhen Huang, 2014. "High-dimensional process monitoring and change point detection using embedding distributions in reproducing kernel Hilbert space," IISE Transactions, Taylor & Francis Journals, vol. 46(10), pages 999-1016, October.
    3. Srivastava, Muni S., 2009. "A test for the mean vector with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 518-532, March.
    4. Suk Joo Bae & Giang Do & Paul Kvam, 2016. "On data depth and the application of nonparametric multivariate statistical process control charts," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(5), pages 660-676, September.
    5. Zou, Changliang & Qiu, Peihua, 2009. "Multivariate Statistical Process Control Using LASSO," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1586-1596.
    6. S. Chakraborti & P. van der Laan & M. A. van de Wiel, 2004. "A class of distribution‐free control charts," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(3), pages 443-462, August.
    7. Srivastava, Muni S. & Du, Meng, 2008. "A test for the mean vector with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 386-402, March.
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