Computational Statistics

, Volume 30, Issue 4, pp 1245–1278 | Cite as

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

  • H. W. You
  • Michael B. C. Khoo
  • P. Castagliola
  • Yanjing Ou
Original Paper

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.

Keywords

Estimation of process parameters Side sensitive group runs \(\bar{{X}}\) chart Group runs \(\bar{{X}}\) chart Synthetic \(\bar{{X}}\) chart \(\bar{{X}}\) chart Conforming run length 

Notes

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • H. W. You
    • 1
  • Michael B. C. Khoo
    • 1
  • P. Castagliola
    • 2
  • Yanjing Ou
    • 3
  1. 1.School of Mathematical SciencesUniversiti Sains MalaysiaPenangMalaysia
  2. 2.LUNAM Université, Université de Nantes & IRCCyN UMR CNRS 6597NantesFrance
  3. 3.Singapore Institute of Manufacturing Technology (SIMTech)SingaporeSingapore

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