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Monitoring Process Mean and Variability with One Non-central Chi-square Chart

Author

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  • A. F. B. Costa
  • M. A. Rahim

Abstract

Traditionally, an X-chart is used to control the process mean and an R-chart to control the process variance. However, these charts are not sensitive to small changes in process parameters. A good alternative to these charts is the exponentially weighted moving average (EWMA) control chart for controlling the process mean and variability, which is very effective in detecting small process disturbances. In this paper, we propose a single chart that is based on the non-central chi-square statistic, which is more effective than the joint X and R charts in detecting assignable cause(s) that change the process mean and/or increase variability. It is also shown that the EWMA control chart based on a non-central chi-square statistic is more effective in detecting both increases and decreases in mean and/or variability.

Suggested Citation

  • A. F. B. Costa & M. A. Rahim, 2004. "Monitoring Process Mean and Variability with One Non-central Chi-square Chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(10), pages 1171-1183.
    • Handle: RePEc:taf:japsta:v:31:y:2004:i:10:p:1171-1183
    DOI: 10.1080/0266476042000285503
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    Citations

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    Cited by:

    1. 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.
    2. Bock, David & Pettersson, Kjell, 2007. "Explorative analysis of spatial aspects on the Swedish influenza data," Research Reports 2007:10, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    3. Bock, David, 2007. "Evaluations of likelihood based surveillance of volatility," Research Reports 2007:9, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    4. Bock, David, 2007. "Consequences of using the probability of a false alarm as the false alarm measure," Research Reports 2007:3, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    5. 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.
    6. David Bock, 2008. "Aspects on the control of false alarms in statistical surveillance and the impact on the return of financial decision systems," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(2), pages 213-227.
    7. 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.

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