An attribute inspection control chart for process mean monitoring

This paper proposes a new control chart, denoted by X−att\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overset{-}{X}}^{att} $$\end{document}, for evaluating the stability of a process mean. This chart is based on attribute inspection rather than physical measurements (taken with an instrument such as a caliper or precise balance) of the quality characteristics of interest of the sampled items. Based on a go–no-go gauge device (which generates five categorizations), the average of a quality characteristic of interest is controlled. In equally spaced times, samples of n items are collected, and the averages are estimated by means of X−att\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overset{-}{X}}^{att} $$\end{document} based solely on the obtained categorization to decide whether the process is in control. Once the distribution of X−att\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overset{-}{X}}^{att} $$\end{document} is calculated, the decision problem is defined in terms of a mathematical programming formulation to find the dimensions to be used in the go–no-go gauge and to find the control limits that minimize the average run length (ARL) for the out-of-control situation and that are constrained to a prefixed ARL for the under-control situation. As shown by extensive computational experiments, the newly introduced X−att\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overset{-}{X}}^{att} $$\end{document} control chart outperforms the conventional X−\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overset{-}{X} $$\end{document} control chart for small shifts in the means and is still competitive otherwise. Because the new X−att\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overset{-}{X}}^{att} $$\end{document} control chart uses attributes, it can be considered a viable alternative to the conventional X−\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overset{-}{X} $$\end{document} control chart.