Phase-I monitoring of high-dimensional covariance matrix using an adaptive thresholding LASSO rule

Abstract

High-dimensional variability monitoring and diagnosing is of great prominence for the quality improvement and cost reduction. Most of the existing control charts are mainly based on the assumption that the in-control covariance matrix is known in prior. This paper proposes a new control chart for monitoring of variability of high-dimensional process under the sparsity conditions. The proposed control chart uses the adaptive thresholding LASSO rule for estimating the unknown covariance matrix. To evaluate the performance of the proposed chart, named as T-COV, the signal probability was estimated under several patterns of out-of-control conditions and compared with the conditional entropy (CE) control chart. This paper uses the process of spur gear production as a real-world example to illustrate the operating procedures of the T-COV chart. The results of the simulation and real studies have revealed the advantage of the T-COV chart over the CE in quickly capturing and precisely diagnosing the deviation in the covariance matrix of the high-dimensional processes.