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A multivariate control chart for simultaneously monitoring process mean and variability

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  • Zhang, Jiujun
  • Li, Zhonghua
  • Wang, Zhaojun

Abstract

Recently, monitoring the process mean and variability simultaneously for multivariate processes by using a single control chart has drawn some attention. However, due to the complexity of multivariate distributions, existing methods in univariate processes cannot be readily extended to multivariate processes. In this paper, we propose a new single control chart which integrates the exponentially weighted moving average (EWMA) procedure with the generalized likelihood ratio (GLR) test for jointly monitoring both the multivariate process mean and variability. Due to the powerful properties of the GLR test and the EWMA procedure, the new chart provides quite robust and satisfactory performance in various cases, including detection of the decrease in variability and individual observation at the sampling point, which are very important cases in many practical applications but may not be well handled by existing approaches in the literature. The application of our proposed method is illustrated by a real data example in ambulatory monitoring.

Suggested Citation

  • Zhang, Jiujun & Li, Zhonghua & Wang, Zhaojun, 2010. "A multivariate control chart for simultaneously monitoring process mean and variability," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2244-2252, October.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:10:p:2244-2252
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    References listed on IDEAS

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    1. Shu, Lianjie & Jiang, Wei & Wu, Zhang, 2008. "Adaptive CUSUM procedures with Markovian mean estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4395-4409, May.
    2. Arthur Yeh & Dennis Lin & Honghong Zhou & Chandramouliswaran Venkataramani, 2003. "A multivariate exponentially weighted moving average control chart for monitoring process variability," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(5), pages 507-536.
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    Cited by:

    1. Mitra, Amitava & Lee, Kang Bok & Chakraborti, Subhabrata, 2019. "An adaptive exponentially weighted moving average-type control chart to monitor the process mean," European Journal of Operational Research, Elsevier, vol. 279(3), pages 902-911.
    2. Hyeon-Ah Kang, 2023. "Sequential Generalized Likelihood Ratio Tests for Online Item Monitoring," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 672-696, June.
    3. Robert Garthoff & Iryna Okhrin & Wolfgang Schmid, 2014. "Statistical surveillance of the mean vector and the covariance matrix of nonlinear time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 225-255, July.
    4. Hamed Sabahno & Seyed Taghi Akhavan Niaki, 2023. "New Machine-Learning Control Charts for Simultaneous Monitoring of Multivariate Normal Process Parameters with Detection and Identification," Mathematics, MDPI, vol. 11(16), pages 1-31, August.
    5. Ahmad, Shabbir & Riaz, Muhammad & Abbasi, Saddam Akber & Lin, Zhengyan, 2013. "On monitoring process variability under double sampling scheme," International Journal of Production Economics, Elsevier, vol. 142(2), pages 388-400.

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