Double Sampling Adaptive Thresholding LASSO Variability Chart for Phase II Monitoring of High-Dimensional Data Streams

Abstract

In many manufacturing or service systems, the product quality and/or process outcome is described in terms of a large number of quality characteristics. Since the use of large sample sizes in such systems imposes significant costs on the manufacturer, the sample size is usually considered smaller than the process dimension. In this condition, which is referred to high-dimensionality, the sample covariance matrix is not a positive semi-definite matrix. Moreover, another issue to establish variability control charts under high-dimensional setting is their speed to detect the process disturbances under both diagonal and off-diagonal shift patterns. To solve these drawbacks, in this study, a double sampling-based adaptive thresholding LASSO control chart called DSATL is developed to monitor the variability matrix of high-dimensional processes under sparsity assumption. The run length distribution of the DSATL chart under seven out-of-control patterns is evaluated taking a different number of quality characteristics into account. The simulation results show that the detectability of the DSATL chart outperforms the classical adaptive thresholding LASSO one under various changes in the process covariance matrix. The results also confirm that the sensitivity of the DSATL chart for real-time detection of covariance matrix anomalies improves as the process dimension increases.