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Side sensitive group runs \(\bar{{X}}\) chart with estimated process parameters

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Abstract

The Side Sensitive Group Runs (SSGR) \(\bar{{X}}\) chart integrates the \(\bar{{X}}\) chart and an extended version of the conforming run length chart. The SSGR \(\bar{{X}}\) chart was developed to detect changes in the process mean. The SSGR \(\bar{{X}}\) chart was proven to be effective for detecting small and moderate shifts compared with the \(\bar{{X}},\) synthetic \(\bar{{X}}\) and group runs \(\bar{{X}}\) charts, when process parameters are known. However, in reality, process parameters, such as the in-control mean and standard deviation are rarely known. Therefore, these process parameters are estimated from an in-control Phase I dataset. In this article, we investigate the performance of the SSGR \(\bar{{X}}\) chart, based on the average run length criterion, when process parameters are estimated. It is shown that differences in the chart’s performance exist, when process parameters are known and when they are estimated, due to the variability in estimating the process parameters. A study is conducted to find the minimum number of Phase I samples required (based on several sample sizes) so that the SSGR \(\bar{{X}}\) chart with estimated process parameters behaves approximately the same as its known process parameters counterpart. To facilitate process monitoring and to avoid the need to use large number of samples in the Phase I process, this research develops an optimization procedure using the Scicoslab program to find suitable optimal charting parameters of the SSGR \(\bar{{X}}\) chart with estimated process parameters. This program can be requested from the first author.

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Acknowledgments

This research is supported by the Universiti Sains Malaysia (USM), Fundamental Research Grant Scheme (FRGS), no. 203/PMATHS/6711322. The authors wish to express their sincere appreciation to the Editor and Referee, for providing useful comments and suggestions, to improve the style and content of this paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia

    H. W. You & Michael B. C. Khoo

  2. LUNAM Université, Université de Nantes & IRCCyN UMR CNRS 6597, Nantes, France

    P. Castagliola

  3. Singapore Institute of Manufacturing Technology (SIMTech), 71 Nanyang Drive, Singapore, 638075, Singapore

    Yanjing Ou

Authors
  1. H. W. You
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  2. Michael B. C. Khoo
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  3. P. Castagliola
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  4. Yanjing Ou
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Corresponding author

Correspondence to Michael B. C. Khoo.

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You, H.W., Khoo, M.B.C., Castagliola, P. et al. Side sensitive group runs \(\bar{{X}}\) chart with estimated process parameters. Comput Stat 30, 1245–1278 (2015). https://doi.org/10.1007/s00180-015-0573-y

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  • DOI: https://doi.org/10.1007/s00180-015-0573-y

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