Research And Optimization On EW-MA Covariance Matrix Control Charts Based On Adaptive Lasso Thresholding

In many manufacturing or service systems,product quality or process results are characterized based on a large number of quality characteristics.In applications with multivariate or high-dimensional matrices,when a change is detected to occur,it is very unlikely that all of the quality characteristics will simultaneously change is very unlikely,meaning that the drift term may occur in only a few elements of the covariance matrix.This means that the drift terms may occur in only a few elements of the covariance matrix,which brings about the nature of sparsity.To address these problems,this thesis combines the idea of adaptive LASSO thresholding to estimate sparse matrix with the traditional EWMA control chart to design an adaptive LASSO thresholding-based EWMA covariance control chart.EWMA covariance control chart(EWMA＿ALT)based on adaptive LASSO threshold is designed and optimized for monitoring the covariance matrix of a high-dimensional process under the assumption of sparsity.Firstly,the paper determines the parameters of the adaptive LASSO threshold method to estimate the sparse matrix by cross-validation method,constructs the EWMA＿ALT control chart with fixed parameters,and evaluates the run length distribution of the EWMA＿ALT chart under six covariance matrix runaway modes considering different numbers of quality features.The simulation results show that the EWMA＿ALT control chart outperforms the classical adaptive LASSO threshold control chart as well as the conventional EWMA covariance control chart in the case of various changes in the process covariance matrix for monitoring.Then,the impact of each parameter on the control chart performance under different offset patterns is analyzed from the statistical process control perspective,revealing the simplicity of tuning the parameters under this method compared to the existing LASSO penalty likelihood ratio-based control charts.Then this paper introduces a design parameter to the EWMA＿ALT control chart for optimization and extends it to a general weighted moving average control chart(GWMA＿ALT)based on an adaptive LASSO threshold.The performance of the two control charts is compared by calculating their ARL values through Monte Carlo simulations,and the results show that the GWMA＿ALT control chart has a significant improvement in monitoring efficiency when the process undergoes medium and small offsets.Finally,the paper investigates the EWMA＿ALT control chart with variable sampling intervals.The performance of the improved control charts using sampling methods with variable sampling intervals versus fixed sampling intervals is compared,and the factors influencing the average alarm time are analyzed using the average alarm time as the comparison index.