Comprehensive review of high-dimensional monitoring methods: trends, insights, and interconnections

High-dimensional data refers to a dataset that contains many variables or features, typically with many more features (𝑝) than observations (𝑛) (i.e., 𝑛 < 𝑝). With technological advancements in sensors, high-dimensional data are becoming increasingly common in process-monitoring applications. Therefore, this study presents a comprehensive overview of high-dimensional monitoring methods, in which 82 articles published from 2004 to 2023 were found to be relevant. The literature on high-dimensional monitoring can be divided into three approaches: control charts based on dimension reduction, variable selection, and high-dimensional techniques. Furthermore, the literature on each approach is divided in terms of control chart structures such as memory-less (Hotelling’s 𝑇 2 ), memory type (multivariate exponentially weighted moving average (MEWMA) and multivariate cumulative sum (MCUSUM)), and others. Real-life datasets from different fields, such as industry, medical science, chemical engineering, and image processing, which have frequently been used in high-dimensional monitoring, are also listed. It is noted that the literature on high-dimensional monitoring increased after 2016, and most studies were designed using high-dimensional techniques. Moreover, most studies proposed memory types and other structures for monitoring high-dimensional data. This review article offers a comprehensive summary of the current state-of-the-art high-dimensional monitoring research and identifies potential areas for future research.