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On the exponentially weighted moving variance

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  • Longcheen Huwang
  • Yi‐Hua Tina Wang
  • Arthur B. Yeh
  • Ze‐Shiang Jason Chen

Abstract

MacGregor and Harris (J Quality Technol 25 (1993) 106–118) proposed the exponentially weighted mean squared deviation (EWMS) and the exponentially weighted moving variance (EWMV) charts as ways of monitoring process variability. These two charts are particularly useful for individual observations where no estimate of variability is available from replicates. However, the control charts derived by using the approximate distributions of the EWMS and EWMV statistics are difficult to interpret in terms of the average run length (ARL). Furthermore, both control charting schemes are biased procedures. In this article, we propose two new control charts by applying a normal approximation to the distributions of the logarithms of the weighted sum of chi squared random variables, which are respectively functions of the EWMS and EWMV statistics. These new control charts are easy to interpret in terms of the ARL. On the basis of the simulation studies, we demonstrate that the proposed charts are superior to the EWMS and EWMV charts and they both are nearly unbiased for the commonly used smoothing constants. We also compare the performance of the proposed charts with that of the change point (CP) CUSUM chart of Acosta‐Mejia (1995). The design of the proposed control charts is discussed. An example is also given to illustrate the applicability of the proposed control charts. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009

Suggested Citation

  • Longcheen Huwang & Yi‐Hua Tina Wang & Arthur B. Yeh & Ze‐Shiang Jason Chen, 2009. "On the exponentially weighted moving variance," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(7), pages 659-668, October.
    • Handle: RePEc:wly:navres:v:56:y:2009:i:7:p:659-668
    DOI: 10.1002/nav.20369
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    References listed on IDEAS

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    1. Ross Sparks, 2003. "Monitoring for Increases in Process Variance," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(4), pages 383-394, December.
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    Cited by:

    1. Xiaobei Shen & Changliang Zou & Wei Jiang & Fugee Tsung, 2013. "Monitoring poisson count data with probability control limits when sample sizes are time varying," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 625-636, December.
    2. Changliang Zou & Zhaojun Wang & Fugee Tsung, 2012. "A spatial rank‐based multivariate EWMA control chart," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(2), pages 91-110, March.

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