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Improved R and s control charts for monitoring the process variance

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  • Guoyi Zhang

Abstract

The Shewhart R control chart and s control chart are widely used to monitor shifts in the process spread. One fact is that the distributions of the range and sample standard deviation are highly skewed. Therefore, the R chart and s chart neither provide an in-control average run length (ARL) of approximately 370 nor guarantee the desired type I error of 0.0027. Another disadvantage of these two charts is their failure in detecting an improvement in the process variability. In order to overcome these shortcomings, we propose the improved R chart (IRC) and s chart (ISC) with accurate approximation of the control limits by using cumulative distribution functions of the sample range and standard deviation. Simulation studies show that the IRC and ISC perform very well. We also compare the type II error risks and ARLs of the IRC and ISC and found that the s chart is generally more efficient than the R chart. Examples are given to illustrate the use of the developed charts.

Suggested Citation

  • Guoyi Zhang, 2014. "Improved R and s control charts for monitoring the process variance," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1260-1273, June.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:6:p:1260-1273
    DOI: 10.1080/02664763.2013.864264
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    References listed on IDEAS

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    1. Athanasios C. Rakitzis & Demetrios L. Antzoulakos, 2011. "On the improvement of one-sided S control charts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2839-2858, February.
    2. Huwang, Longcheen & Huang, Chun-Jung & Wang, Yi-Hua Tina, 2010. "New EWMA control charts for monitoring process dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2328-2342, October.
    3. Lee, Pei-Hsi, 2011. "Adaptive R charts with variable parameters," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 2003-2010, May.
    4. 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.
    5. Pandu R. Tadikamalla & Dana G. Popescu, 2007. "Kurtosis correction method for X̄ and R control charts for long‐tailed symmetrical distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 371-383, June.
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