The absence of directional sensitivity can limit the charts’ application, particularly when users are interested in detecting variations in one direction than the other. They are designed to detect shifts in both upper and downward directions with equal precision when monitoring the process mean vector. Multivariate memory-type control charts that use information from both the current and previous process observations have been proposed. Applications on two real datasets are given to illustrate the implementation of the AMEWMA-III chart in comparison to the AMEWMA-I and AMEWMA-II charts. Additionally, the AMEWMA-III chart outperforms the AMEWMA-I and AMEWMA-II charts for moderate-to-large shifts but for small-to-moderate shifts, all the AMEWMA charts have similar performances. The AMEWMA-III chart surpasses the MEWMA chart for small and moderate shifts whilst the latter with a larger smoothing parameter prevails over the former for large shifts. A Monte Carlo simulation is used to compute the run length characteristics of the MEWMA, AMEWMA-I, AMEWMA-II, and AMEWMA-III charts. In this research, a new partially parameter-free adaptive MEWMA (AMEWMA) chart, called the AMEWMA-III chart, which does not contain any control chart parameter (except the control limit) is developed to monitor the mean vector of a process that follows a multivariate normal distribution. The run length performances of adaptive/nonadaptive multivariate exponentially weighted moving average (MEWMA) charts depend on the smoothing parameter.
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