Effect of sample size on the performance of Shewhart control charts View Full Text


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Article Info

DATE

2016-09-19

AUTHORS

Salah Haridy, Ahmed Maged, Saleh Kaytbay, Sherif Araby

ABSTRACT

The control chart is one of the most powerful techniques in statistical process control (SPC) to monitor processes and ensure quality. The sample size n plays a critical role in the overall performance of any control chart. This article studies the effect of n on the performance of Shewhart control charts, which have traditionally been used for monitoring both the mean and variance of a variable (e.g., the diameter of a shaft and the temperature of a surface). The study is conducted under different combinations of false alarm rate and process shift. The detection speed of the Shewhart charts is evaluated in terms of average extra quadratic loss (AEQL) which is a measure of the overall performance. It is found that n = 2 is the best sample size of the Shewhart X_&R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overset{\_}{\boldsymbol{X}}\&\boldsymbol{R} $$\end{document} and X_&S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overset{\_}{\boldsymbol{X}}\&\boldsymbol{S} $$\end{document} charts. The comparative study reveals that the X_&R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overset{\_}{\boldsymbol{X}}\&\boldsymbol{R} $$\end{document} and X_&S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overset{\_}{\boldsymbol{X}}\&\boldsymbol{S} $$\end{document} charts with n = 2 outperform the X_&R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overset{\_}{\boldsymbol{X}}\&\boldsymbol{R} $$\end{document} and X_&S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overset{\_}{\boldsymbol{X}}\&\boldsymbol{S} $$\end{document} charts with n ≥ 4 by at least 9 and 7 %, respectively, in terms of AEQL. These results contradict the common knowledge in SPC niche that n between 4 and 6 is usually recommended for the X_&R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overset{\_}{\boldsymbol{X}}\&\boldsymbol{R} $$\end{document} and X_&S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overset{\_}{\boldsymbol{X}}\&\boldsymbol{S} $$\end{document} charts. More... »

PAGES

1177-1185

References to SciGraph publications

  • 2006-07. Statistical design of variable sample size and sampling intervalcontrol charts with run rulescontrol charts with run rules in THE INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY
  • 2012-08-24. The variable sample size t control chart for monitoring short production runs in THE INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY
  • 2014-06-20. An optimization design of the 3-EWMA scheme for monitoring mean shifts in THE INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY
  • 2014-11-23. Designing of a hybrid exponentially weighted moving average control chart using repetitive sampling in THE INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY
  • 2010-07-21. An integrated framework of statistical process control and design of experiments for optimizing wire electrochemical turning process in THE INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY
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