Multivariate memory-type control charts that use information from both the current and previous process observations have been proposed. They are designed to detect shifts in both upper and downward directions with equal precision when monitoring the process mean vector. The absence of directional sensitivity can limit the charts' application, particularly when users are interested in detecting variations in one direction than the other. This article proposes one-sided and two one-sided multivariate control charts for monitoring shifts in the process mean vector. The proposed charts are presented in the form of the multivariate homogeneously weighted moving average approach that yields efficient detection of shifts in the mean vector. We provide simulation studies under different shift sizes in the process mean vector and evaluate the performance of the proposed charts in terms of their run length properties. We compare the average run length (ARL) results of the charts with the conventional charts as well as the onesided and two one-sided multivariate exponentially weighted moving average (MEWMA) and multivariate cumulative sum (MCUSUM) charts. Our simulation results show that the proposed charts outperform the existing charts used for the same purpose, particularly when interest lies in detecting small shifts in the mean vector. We show how the charts can be designed to be robust to non-normal distributions and give a step-by-step implementation efficient application of the charts when their parameters are unknown and need to be estimated. Finally, an illustrative example is provided to show the application of the proposed charts.INDEX TERMS Average run length; multivariate homogeneously weighted moving average; one-sided control charts; two one-sided control charts, robustness, estimation.

One‐sided control charts for monitoring changes in the mean level are proposed in this paper. The proposed charts are given in the form of a homogeneously weighted moving average technique that provides efficient monitoring of small shifts in the mean level. The charts accumulate observations that are above the target (or mean value) and truncated the observations that are less than the target to the target value in their computations. Average run length comparisons of the proposed charts with the existing one‐sided charts, based on the exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts, show that the proposed charts are more efficient in detecting small shifts than the competing charts. We investigate the sensitivity of the charts to non‐normality and show how they can be designed to be robust to non‐normal distributions. We provide a step‐by‐step implementation of the proposed charts when their parameters are unknown and estimated from historical reference data sets. The advantage of the proposed charts over some existing one‐sided charts is demonstrated via an illustrative example, involving monitoring mean lethal concentration (LC50) from a k‐nearest neighbours (KNN) regression‐based Quantitative Structure‐Activity Relationships (QSAR) model that relates LC50 to eight molecular descriptors.