Max-Half-Mchart: A Simultaneous Control Chart Using a Half-Normal Distribution for Subgroup Observations

A Simultaneous control chart is a well-known tool for monitoring the process mean and process variability with a single chart. In recent decades, many researchers have been interested in developing simultaneous control charts. The Shewhart chart is the most common and simple simultaneous control chart. The Multivariate Maximum control chart (Max-Mchart) is a type Shewhart chart that simultaneously monitors the process of multivariate data. This paper proposes a new transformation using a half-normal distribution to improve the Max-chart performance for subgroup observations. The new proposed chart is called Max-Half-Mchart. The Average Run Length (ARL) results show that the proposed Max-Half-Mchart outperforms the Max-Mchart. Additionally, in real data scenarios, the proposed Max-Half-Mchart is consistent with the statistic in the Hotelling T
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chart and the Generalized Variance (GV) chart.