Adaptive LASSO‐Based Robust Multivariate Process Monitoring and Diagnostics

ABSTRACT Statistical process control (SPC) charts are commonly utilized across various fields to identify distributional shifts within sequential processes. Conventional SPC charts typically assume that in‐control (IC) process observations are independent and identically distributed across different observation times, typically conforming to a parametric distribution such as the normal distribution. Nonetheless, these assumptions frequently do not hold in applications. In addition, in multivariate SPC applications, process mean vectors often shift in only one or a small number of components, which is termed a sparse shift. To overcome these challenges, we develop a general framework for process monitoring and diagnostics, alongside the development of two robust control charts, which are robust to the IC process distribution, serial correlation, and sparse shifts. Our approach integrates techniques for data decorrelation and transformation, along with variable selection via the least absolute shrinkage and selection operator (LASSO) method. It is shown that the proposed method effectively handles serial correlations and nonparametric IC process distributions, effectively detecting shifts of various magnitudes and directions. Moreover, it provides real‐time diagnostics that not only estimate the position of shifts but also identify the specific variables that have shifted. Therefore, the proposed methods provide a powerful tool for monitoring multivariate processes in various fields.