An Efficient Online Monitoring Method for High‐Dimensional Data Based on Interpoint Distance Algorithm

ABSTRACT With the continued development of modern monitoring technology, high‐dimensional (HD) structures have become more commonplace. However, HD data can be complex, often making traditional monitoring methods invalid. Therefore, designing efficient HD monitoring schemes remains a challenging practical problem. This paper introduces two conditionally distribution‐free exponentially weighted moving average (EWMA) control charts that utilizing interpoint distances to monitor HD processes. Previous approaches rely predominantly on parametric methods or dimension‐reduction methods, which are often misspecified. In contrast, we propose a novel EWMA control chart based on the Cucconi statistic to jointly monitor the location and scale parameters of the process in a nonparametric manner. To enhance monitoring efficiency, we further develop an adaptive version of this EWMA control chart. The adaptively weighted method is not only widely applicable in the distribution‐free setting, but also maintains excellent monitoring performance. The advantages of our method are demonstrated by Monte Carlo simulations, where we observe that our approach outperforms comparable methods in the correlated‐data setting and when the sample size is small relative to the data dimension. Finally, a real‐data application to semiconductor manufacturing demonstrates the effectiveness of our scheme.