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Adaptive CUSUM procedures with Markovian mean estimation

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  • Shu, Lianjie
  • Jiang, Wei
  • Wu, Zhang

Abstract

This paper proposes using a Markovian-type mean estimating procedure in the conventional cumulative sum (CUSUM) control scheme to update its reference value in an adaptive way. This generalizes a class of Markovian adaptive CUSUM (ACUSUM) schemes to achieve the aim of providing an overall good performance over a range of future expected but unknown mean shifts. A two-dimensional Markov chain model is developed to analyze the run length performance of the new scheme. A comparison of run length performance of the proposed ACUSUM scheme and other control charts is shown favorable to the former.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:9:p:4395-4409
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    Citations

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    Cited by:

    1. 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.
    2. Su, Yan & Shu, Lianjie & Tsui, Kwok-Leung, 2011. "Adaptive EWMA procedures for monitoring processes subject to linear drifts," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2819-2829, October.
    3. Lee, Pei-Hsi, 2011. "Adaptive R charts with variable parameters," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 2003-2010, May.
    4. Wu, Zhang & Yang, Mei & Jiang, Wei & Khoo, Michael B.C., 2008. "Optimization designs of the combined Shewhart-CUSUM control charts," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 496-506, December.
    5. Pei-Hsi Lee & Yi-Hsien Huang & Tsen-I Kuo & Ching-Cheng Wang, 2013. "The effect of the individual chart with variable control limits on the river pollution monitoring," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(4), pages 1803-1812, June.
    6. Sánchez, Ismael, 2015. "Adaptive EWMA Control Charts with a Time Varying Smoothing Parameter," DES - Working Papers. Statistics and Econometrics. WS ws1507, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. 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.
    8. Luo, Yunzhao & Li, Zhonghua & Wang, Zhaojun, 2009. "Adaptive CUSUM control chart with variable sampling intervals," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2693-2701, May.
    9. Zhang, Min & Nie, Guohua & He, Zhen, 2014. "Performance of cumulative count of conforming chart of variable sampling intervals with estimated control limits," International Journal of Production Economics, Elsevier, vol. 150(C), pages 114-124.
    10. Maravelakis, Petros E. & Castagliola, Philippe, 2009. "An EWMA chart for monitoring the process standard deviation when parameters are estimated," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2653-2664, May.

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