Design Of Multivariate Control Chart Based On Nonparametric Test And Variable Selection

"Made in China 2025" promotes the process of industrial informatization.Using data to solve product quality problems is a hot issue in current industrial production.The control chart is an important means for quality management.It can effectively monitor the product process and alert in time to abnormal fluctuations of product.Currently,there are many types of data collected in industrial production,with high data dimensions,unknown data distribution,unknown variable correlation,and few controlled samples.Faced with such data,traditional control charts are not effective.Mean shift is a common problem in quality monitoring.There are two cases of mean shift: mean sparse shift and mean non-sparse shift.Two multivariate nonparametric control charts were designed using nonparametric tests and variable selection methods to monitor these two situations respectively.Run test is an important non-parametric test method.Based on the run test,a multivariate non-parametric control chart HAMEWMA is designed.First,using the idea of Kruskal algorithm,the observations are arranged into the shortest Hamiltonian path;Second,based on the number of runs in the shortest Hamiltonian path,an EWMA structure control chart with sliding windows is designed.Monte Carlo simulation experiments and comparison with multivariate nonparametric control charts(DFEWMA,SREWMA,SSEWMA,RTC)show that the monitoring performance is better when the mean drift is large and the data distribution is non-normal.A multivariate non-parametric control chart SEEWMA is designed based on the spatial sign test in the non-parametric test method and the Elastic Net method in the variable selection method.Firstly,the observed values are affine-transformed by using spatial sign test;secondly,Elastic Net is used to estimate the mean shift,and the important variables that may shift are screened to construct the EWMA structure control chart.Compared with the multivariate control charts(LEWMA,MDSE,SLEWMA),it shows that SEEWMA has strong monitoring ability for the sparse shift of normal and non-normal distribution data,and it can effectively monitor the small mean shift.In the real case study,the data of semiconductor production and white wine production are analyzed,and the proposed control chart can quickly detect abnormal fluctuations and promptly report the alarm.Finally,the two multivariate non-parametric control charts proposed in this paper are complementary to monitoring under different mean shift conditions.HAMEWMA performs better in the mean non-sparse shift,and SEEWMA performs better in the mean sparse shift.