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An enhanced adaptive CUSUM control chart

Author

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  • Zhang Wu
  • Jianxin Jiao
  • Mei Yang
  • Ying Liu
  • Zhaojun Wang

Abstract

Adaptive CUSUM charts, referred to as ACUSUM charts, have attracted considerable attention from the research community. By adjusting the reference parameter k dynamically, an ACUSUM chart may achieve a better performance over a range of mean shifts than conventional CUSUM charts that are designed for maximal detection effectiveness at a particular level of process shift. This article studies a new feature of the ACUSUM chart related to an additional charting parameter w, i.e., the exponential of the sample mean shift in (xt – μ0)w. The ACUSUM chart can be enhanced by adapting this parameter w according to the on-line estimated value of the mean shift, in conjunction with the reference parameter k. The testing cases reveal that this new adaptive CUSUM chart not only outperforms the earlier ACUSUM chart to a substantial degree, but also works as well as the most effective combined schemes consisting of a few CUSUM and/or charts. Furthermore, this enhanced ACUSUM chart is easier to design and implement in a computerized environment compared with those combined schemes. In addition, a general-purpose optimization algorithm is proposed to assist the designs of various CUSUM charts. This paper demonstrates that this algorithm can significantly improve the performance of many CUSUM charts over the entire process shift range. Moreover, a systematic performance comparison of eight CUSUM charts is presented. The findings from this comparison are useful aids for SPC practitioners to select an appropriate CUSUM chart for real applications.[Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplementary resource: Appendix]

Suggested Citation

  • Zhang Wu & Jianxin Jiao & Mei Yang & Ying Liu & Zhaojun Wang, 2009. "An enhanced adaptive CUSUM control chart," IISE Transactions, Taylor & Francis Journals, vol. 41(7), pages 642-653.
    • Handle: RePEc:taf:uiiexx:v:41:y:2009:i:7:p:642-653
    DOI: 10.1080/07408170802712582
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    Citations

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    Cited by:

    1. Lim, S.L. & Khoo, Michael B.C. & Teoh, W.L. & Xie, M., 2015. "Optimal designs of the variable sample size and sampling interval X¯ chart when process parameters are estimated," International Journal of Production Economics, Elsevier, vol. 166(C), pages 20-35.
    2. Ou, Yanjing & Wu, Zhang & Goh, Thong Ngee, 2011. "A new SPRT chart for monitoring process mean and variance," International Journal of Production Economics, Elsevier, vol. 132(2), pages 303-314, August.
    3. Khoo, Michael B.C. & Teoh, W.L. & Castagliola, Philippe & Lee, M.H., 2013. "Optimal designs of the double sampling X¯ chart with estimated parameters," International Journal of Production Economics, Elsevier, vol. 144(1), pages 345-357.
    4. 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.
    5. Muhammad Riaz & Babar Zaman & Ishaq Adeyanju Raji & M. Hafidz Omar & Rashid Mehmood & Nasir Abbas, 2022. "An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector," Mathematics, MDPI, vol. 10(12), pages 1-27, June.
    6. 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.
    7. Nasir Abbas & Muhammad Riaz & Shabbir Ahmad & Muhammad Abid & Babar Zaman, 2020. "On the Efficient Monitoring of Multivariate Processes with Unknown Parameters," Mathematics, MDPI, vol. 8(5), pages 1-32, May.
    8. Ahmad, Shabbir & Riaz, Muhammad & Abbasi, Saddam Akber & Lin, Zhengyan, 2013. "On monitoring process variability under double sampling scheme," International Journal of Production Economics, Elsevier, vol. 142(2), pages 388-400.
    9. Costa, Antonio Fernando Branco & Machado, Marcela Aparecida Guerreiro, 2011. "Variable parameter and double sampling charts in the presence of correlation: The Markov chain approach," International Journal of Production Economics, Elsevier, vol. 130(2), pages 224-229, April.
    10. Imad Khan & Muhammad Noor-ul-Amin & Dost Muhammad Khan & Salman A. AlQahtani & Mostafa Dahshan & Umair Khalil, 2023. "Monitoring of Location Parameters with a Measurement Error under the Bayesian Approach Using Ranked-Based Sampling Designs with Applications in Industrial Engineering," Sustainability, MDPI, vol. 15(8), pages 1-18, April.

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