Tr(R2) control charts based on kernel density estimation for monitoring multivariate variability process

Abstract

The multivariate control charts are not only used to monitor the mean vector but also can be used to monitor the covariance matrix. The multivariate variability charts are used to guarantee the consistency of products in the subgroup. Many researchers have been studied the multivariate control chart for variability. Nevertheless, those conventional methods have several drawbacks because it is developed based on the determinant of the covariance matrix and not free of the measurement unit. To overcome such issues, this paper proposes the multivariate control chart for variability based on trace of the squared correlation matrix. Kernel Density Estimation is used to improve estimated control limit. The kernel density estimation method is used to calculate the control limit. Through simulation studies, the performance of the proposed chart is evaluated using the average run length (ARL). The control limits of the proposed chart are produced in control ARL at about 370 for α = 0.00273. Meanwhile, the proposed chart demonstrated better performance to detect the shift for the large value of quality characteristics and sample size. The proposed chart also produces a better performance than the conventional generalized variance chart when used to monitor the real case data.

Keywords

• multivariate variability process
• trace squared correlation matrix
• control chart
• kernel density estimation
• average run length