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A control chart based on likelihood ratio test for detecting patterned mean and variance shifts

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  • Zhou, Qin
  • Luo, Yunzhao
  • Wang, Zhaojun

Abstract

Control charts based on generalized likelihood ratio test (GLRT) are attractive from both theoretical and practical points of view. Most of the existing works in the literature focusing on the detection of the process mean and variance are almost based on the assumption that the shifts remain constant over time. The case of the patterned mean and variance changes may not be well discussed. In this research, we propose a new control chart which integrates the exponentially weighted moving average (EWMA) procedure with the GLRT statistics to monitor the process with patterned mean and variance shifts. The attractive advantage of our control chart is its reference-free property. Due to the good properties of GLRT and EWMA procedures, our simulation results show that the proposed chart provides quite effective and robust detecting ability for various types of shifts. The implementation of our proposed control chart is illustrated by a real data example from chemical process control.

Suggested Citation

  • Zhou, Qin & Luo, Yunzhao & Wang, Zhaojun, 2010. "A control chart based on likelihood ratio test for detecting patterned mean and variance shifts," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1634-1645, June.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:6:p:1634-1645
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    References listed on IDEAS

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    Cited by:

    1. Marianne Frisén, 2014. "Spatial outbreak detection based on inference principles for multivariate surveillance," IISE Transactions, Taylor & Francis Journals, vol. 46(8), pages 759-769, August.
    2. Linus Schiöler & Marianne Fris�n, 2012. "Multivariate outbreak detection," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 223-242, April.
    3. Huang, Wenpo & Shu, Lianjie & Jiang, Wei, 2012. "Evaluation of exponentially weighted moving variance control chart subject to linear drifts," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4278-4289.
    4. Wang, Kaibo & Yeh, Arthur B. & Li, Bo, 2014. "Simultaneous monitoring of process mean vector and covariance matrix via penalized likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 206-217.
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    6. Huwang, Longcheen & Huang, Chun-Jung & Wang, Yi-Hua Tina, 2010. "New EWMA control charts for monitoring process dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2328-2342, October.

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