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In this article, we develop a new Triple EWMA-Max (TEWMA-Max) control chart for joint monitoring of the process mean and variance. The run-length characteristics of the proposed chart are computed through Monte-Carlo simulations. A detailed comparative study is conducted to compare the performance of the proposed chart with that of the EWMA-Max and DEWMA-Max charts. The comparison results reveal that the TEWMA-Max chart is more sensitive than the EWMA-Max chart in detecting small to moderate shifts in the mean and variability. Furthermore, it is more efficient than the DEWMA-Max chart for small to moderate shifts in the mean and small to large downward and large upward shifts in the dispersion, while it is quite comparable for small upward shifts in the variability with an increase of the smoothing parameter  λ . Additionally, the TEWMA-Max chart shows a satisfactory overall performance for detecting a wide range of shift combinations in the process mean and dispersion. Finally, real and simulated datasets are considered to present the implementation of the new chart.

A joint monitoring of the process mean and variance with a TEWMA-Max control chart