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Evaluation of exponentially weighted moving variance control chart subject to linear drifts

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  • Huang, Wenpo
  • Shu, Lianjie
  • Jiang, Wei

Abstract

The exponentially weighted moving average chart of the squared deviation (EWMAS) is often applied for monitoring changes such as step shifts and linear drifts in process variation when no subgrouping is available. This paper analyzes the performance of the EWMAS chart under drifts in process variation. A fast and accurate algorithm based on the piecewise collocation method is presented for computing both the zero-state and steady-state average run lengths of the EWMAS chart. It is shown that the proposed method can provide accurate approximation results in both zero-state and steady-state cases. Some optimal design tables are also provided to facilitate the design of EWMAS charts in practice.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4278-4289
    DOI: 10.1016/j.csda.2012.04.013
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    References listed on IDEAS

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    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. 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.
    4. Li, Zhonghua & Wang, Zhaojun & Wu, Zhang, 2009. "Necessary and sufficient conditions for non-interaction of a pair of one-sided EWMA schemes with reflecting boundaries," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 368-374, February.
    5. Michael Khoo & Zhang Wu & Chung-Ho Chen & Kah Yeong, 2010. "Using one EWMA chart to jointly monitor the process mean and variance," Computational Statistics, Springer, vol. 25(2), pages 299-316, June.
    6. Knoth, Sven, 2006. "Computation of the ARL for CUSUM-S2 schemes," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 499-512, November.
    7. 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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