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A Variable Sampling Interval Synthetic Xbar Chart for the Process Mean

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  • Lei Yong Lee
  • Michael Boon Chong Khoo
  • Sin Yin Teh
  • Ming Ha Lee

Abstract

The usual practice of using a control chart to monitor a process is to take samples from the process with fixed sampling interval (FSI). In this paper, a synthetic X¯ control chart with the variable sampling interval (VSI) feature is proposed for monitoring changes in the process mean. The VSI synthetic X¯ chart integrates the VSI X¯ chart and the VSI conforming run length (CRL) chart. The proposed VSI synthetic X¯ chart is evaluated using the average time to signal (ATS) criterion. The optimal charting parameters of the proposed chart are obtained by minimizing the out-of-control ATS for a desired shift. Comparisons between the VSI synthetic X¯ chart and the existing X¯, synthetic X¯, VSI X¯ and EWMA X¯ charts, in terms of ATS, are made. The ATS results show that the VSI synthetic X¯ chart outperforms the other X¯ type charts for detecting moderate and large shifts. An illustrative example is also presented to explain the application of the VSI synthetic X¯ chart.

Suggested Citation

  • 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.
    • Handle: RePEc:plo:pone00:0126331
    DOI: 10.1371/journal.pone.0126331
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    References listed on IDEAS

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    1. Yeong, Wai Chung & Khoo, Michael B.C. & Lee, Ming Ha & Rahim, M.A., 2013. "Economic and economic statistical designs of the synthetic X¯ chart using loss functions," European Journal of Operational Research, Elsevier, vol. 228(3), pages 571-581.
    2. Michael Khoo & V. Wong & Zhang Wu & Philippe Castagliola, 2012. "Optimal design of the synthetic chart for the process mean based on median run length," IISE Transactions, Taylor & Francis Journals, vol. 44(9), pages 765-779.
    3. Santiago Omar Caballero Morales, 2013. "Economic Statistical Design of Integrated X-bar-S Control Chart with Preventive Maintenance and General Failure Distribution," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-25, March.
    4. Wei Lin Teoh & Michael B C Khoo & Sin Yin Teh, 2013. "Optimal Designs of the Median Run Length Based Double Sampling X̄ Chart for Minimizing the Average Sample Size," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-11, July.
    5. Bersimis, Sotiris & Koutras, Markos V. & Maravelakis, Petros E., 2014. "A compound control chart for monitoring and controlling high quality processes," European Journal of Operational Research, Elsevier, vol. 233(3), pages 595-603.
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    7. 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.
    8. Ying Zhang & Philippe Castagliola & Zhang Wu & Michael Khoo, 2011. "The synthetic [Xbar] chart with estimated parameters," IISE Transactions, Taylor & Francis Journals, vol. 43(9), pages 676-687.
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