Malela-Majika, Jean-ClaudeHuman, Schalk WilliamChatterjee, Kashinath2025-02-052025-02-052024-03Malela-Majika, J.-C.; Human, S.W.; Chatterjee, K. HomogeneouslyWeighted Moving Average Control Charts: Overview, Controversies, and New Directions. Mathematics 2024, 12, 637. https://DOI.org/10.3390/math12050637.2227-739010.3390/math12050637http://hdl.handle.net/2263/100547The homogeneously weighted moving average (HWMA) chart is a recent control chart that has attracted the attention of many researchers in statistical process control (SPC). The HWMA statistic assigns a higher weight to the most recent sample, and the rest is divided equally between the previous samples. This weight structure makes the HWMA chart more sensitive to small shifts in the process parameters when running in zero-state mode. Many scholars have reported its superiority over the existing charts when the process runs in zero-state mode. However, several authors have criticized the HWMA chart by pointing out its poor performance in steady-state mode due to its weighting structure, which does not reportedly comply with the SPC standards. This paper reviews and discusses all research works on HWMA-related charts (i.e., 55 publications) and provides future research ideas and new directions.en© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.Homogeneously weighted moving averageDouble HWMAConditional expected delayMemory-type chartMonte Carlo simulationSteady-state modeTriple HWMAWeight structureZero-state modeHomogeneously weighted moving average (HWMA)Statistical process control (SPC)Article