A trimmed EWMA control charts for non-normal processes

The traditional exponentially weighted moving average (EWMA) control chart is very popular in statistical process control (SPC) for detecting small shifts in process mean and variance. It performs well under the assumption of normality but when data violate this assumption, a modified approach is needed. In this paper, we proposed a variable control chart for monitoring the process mean by modifying the traditional EWMA control chart for non-normal processes based on the modified trimmed standard deviation (MTSD). The proposed EWMA control charts are based on three different heuristic methods, namely, the Trimmed Exponentially Weighted Moving Average (T-EWMA) control chart, the Trimmed Weighted Standard Deviation Exponentially Weighted Moving Average (TWSD-EWMA) control chart and the Trimmed Weighted Variance Exponentially Weighted Moving Average (TWV-EWMA) control chart. The performances of the control charts under study are evaluated via a Monte-Carlo simulation study by calculating expected out-of-control points and expected widths under non-normal distributions (i.e. Gamma and Exponential). Also, since the EWMA statistic Zi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Z}_{i}$$\end{document} is sensitive to detect mean shifts in the process, the out-of-control average run length (ARL1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ARL}_{1}$$\end{document}) is considered in the simulation as a best tool to measure the sensitivity. The simulation studies are being carried out for the purpose and results showed that the proposed trimmed control charts performed well for non-normal processes in terms of their shorter expected widths, more number of expected out-of-control points and quick out-of-control signals as compared to non-trimmed versions of control charts. Moreover it is also observed that as weighing constant λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document} increases, the sensitivity of the proposed trimmed control charts increases. For illustration purposes, a real-life data set from a public service industry is analyzed which confirming our conclusions from the simulation analysis. Consequently, for estimating of the process mean when the distribution of the data is non-normal, we recommend the trimmed versions of EWMA control charts for the practitioners to be used.