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Adaptive EWMA procedures for monitoring processes subject to linear drifts

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  • Su, Yan
  • Shu, Lianjie
  • Tsui, Kwok-Leung

Abstract

The conventional Statistical Process Control (SPC) techniques have been focused mostly on the detection of step changes in process means. However, there are often settings for monitoring linear drifts in process means, e.g., the gradual change due to tool wear or similar causes. The adaptive exponentially weighted moving average (AEWMA) procedures proposed by Yashchin (1995) have received a great deal of attention mainly for estimating and monitoring step mean shifts. This paper analyzes the performance of AEWMA schemes in signaling linear drifts. A numerical procedure based on the integral equation approach is presented for computing the average run length (ARL) of AEWMA charts under linear drifts in the mean. The comparison results favor the AEWMA chart under linear drifts. Some guidelines for designing AEWMA charts for detecting linear drifts are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:10:p:2819-2829
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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. Sheng-Tsaing Tseng & Bo-Yan Jou & Chuan-Hao Liao, 2010. "Adaptive variable EWMA controller for drifted processes," IISE Transactions, Taylor & Francis Journals, vol. 42(4), pages 247-259.
    3. Changliang Zou & Yukun Liu & Zhaojun Wang, 2009. "Comparisons of control schemes for monitoring the means of processes subject to drifts," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(2), pages 141-163, September.
    4. A. F. Bissell, 1984. "The Performance of Control Charts and Cusums Under Linear Trend," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(2), pages 145-151, June.
    5. F. F. Gan, 1996. "Average Run Lengths for Cumulative Sum Control Charts Under Linear Trend," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(4), pages 505-512, December.
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    Cited by:

    1. 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.
    2. Chang Zhiyuan & Sun Jinsheng, 2017. "AEWMA t Control Chart for Short Production Runs," Journal of Systems Science and Information, De Gruyter, vol. 4(5), pages 444-459, October.
    3. Graham, M.A. & Mukherjee, A. & Chakraborti, S., 2012. "Distribution-free exponentially weighted moving average control charts for monitoring unknown location," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2539-2561.
    4. Chenglong Li & Qin Su & Min Xie, 2016. "Economic modelling for statistical process control subject to a general quality deterioration," International Journal of Production Research, Taylor & Francis Journals, vol. 54(6), pages 1753-1770, March.

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