IMPROVED ADAPTIVE THRESHOLDING LASSO CHART FOR MONITORING DISPERSION OF HIGHDIMENSIONAL PROCESSES USING GENERALIZED MULTIPLE DEPENDENT STATE SAMPLING

In many applications of multivariate statistical quality control, it is commonly observed that the number of quality characteristics exceeds the sample size. This poses significant challenges in monitoring high-dimensional data. In such conditions, it is challenging to detect sparse changes where an assignable cause leads to the deviation of only a few elements in the covariance matrix. On the other hand, the utilization of the multiple dependent state (MDS) sampling technique to enhance the sensitivity of control charts has recently attracted the attention of researchers. However, to the best of the authors' knowledge, no previous research has been conducted on equipping multivariate dispersion control charting methods with the MDS technique under high dimensionality. Therefore, this article integrates the adaptive thresholding Lasso statistic with the MDS and generalized MDS techniques to track all types of disturbances in the covariance matrix of high-dimensional processes, including diagonal, off-diagonal, and joint diagonal/off-diagonal deviations. The performance of the proposed control charts will be compared through a numerical example under seven out-of-control patterns in terms of three metrics: average, standard deviation, and median of run length. The results clearly indicate that the use of both sampling techniques significantly improves the run length properties of the adaptive thresholding Lasso chart.