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Optimization designs of the combined Shewhart-CUSUM control charts

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Listed:
  • Wu, Zhang
  • Yang, Mei
  • Jiang, Wei
  • Khoo, Michael B.C.

Abstract

This article presents the optimization design of the combined Shewhart chart and CUSUM chart ( chart in short) used in Statistical Process Control (SPC). While the optimization design effectively improves the overall performance of the chart over the entire process shift range, it does not increase difficulties in understanding and implementing this combined chart. A new feature pertaining to an additional charting parameter w (the exponential of the sample mean shift) is also investigated, with the hope of further enhancing the detection effectiveness of the chart. Moreover, this article provides the SPC practitioners with a design table to facilitate the designs of the charts. From this design table, the users can directly find the optimal values of the charting parameters, according to the design specifications. The design table makes the design of an chart as simple as the design of the simplest chart. In general, this article will help to enhance the detection effectiveness of the chart, and facilitate and promote its applications in SPC.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:2:p:496-506
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    References listed on IDEAS

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    1. Fong-jung Yu & Jiang-liang Hou, 2006. "Optimization of design parameters for [image omitted] control charts with multiple assignable causes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(3), pages 279-290.
    2. Messaoud, Amor & Weihs, Claus & Hering, Franz, 2008. "Detection of chatter vibration in a drilling process using multivariate control charts," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3208-3219, February.
    3. G. Yi & S. Coleman & Q. Ren, 2006. "CUSUM method in predicting regime shifts and its performance in different stock markets allowing for transaction fees," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(7), pages 647-661.
    4. Luceno, Alberto & Puig-Pey, Jaime, 2002. "An accurate algorithm to compute the run length probability distribution, and its convolutions, for a Cusum chart to control normal mean," Computational Statistics & Data Analysis, Elsevier, vol. 38(3), pages 249-261, January.
    5. 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.
    6. Jarrett, Jeffrey E. & Pan, Xia, 2007. "The quality control chart for monitoring multivariate autocorrelated processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3862-3870, May.
    7. Zhang Wu & Yu Tian & Sheng Zhang, 2005. "Adjusted-loss-function charts with variable sample sizes and sampling intervals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(3), pages 221-242.
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    Cited by:

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    2. Ou, Yanjing & Wu, Zhang & Tsung, Fugee, 2012. "A comparison study of effectiveness and robustness of control charts for monitoring process mean," International Journal of Production Economics, Elsevier, vol. 135(1), pages 479-490.
    3. Yafen Liu & Zhen He & M. Shamsuzzaman & Zhang Wu, 2010. "A combined control scheme for monitoring the frequency and size of an attribute event," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(12), pages 1991-2013.
    4. Lee, Pei-Hsi, 2013. "Joint statistical design of X¯ and s charts with combined double sampling and variable sampling interval," European Journal of Operational Research, Elsevier, vol. 225(2), pages 285-297.
    5. Wu, Zhang & Yang, Mei & Khoo, Michael B.C. & Castagliola, Philippe, 2011. "What are the best sample sizes for the Xbar and CUSUM charts?," International Journal of Production Economics, Elsevier, vol. 131(2), pages 650-662, June.
    6. 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.
    7. Lei Yong Lee & Michael Boon Chong Khoo & Sin Yin Teh & Ming Ha Lee, 2015. "A Variable Sampling Interval Synthetic Xbar Chart for the Process Mean," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-18, May.

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