On the multivariate progressive control chart for effective monitoring of covariance matrix

With the development of modern acquisition techniques, data with several correlated quality characteristics are increasingly accessible. Thus, multivariate control charts can be employed to detect changes in the process. This study proposes two multivariate control charts for monitoring process variability (MPVC) using a progressive approach. First, when the process parameters are known, the performance of the MPVC charts is compared with some multivariate dispersion schemes. The results showed that the proposed MPVC charts outperform their counterparts irrespective of the shifts in the process dispersion. The effects of the Phase I estimated covariance matrix on the efficiency of the MPVC charts were also evaluated. The performances of the proposed methods and their counterparts are evaluated by calculating some useful run length properties. An application of the proposed chart is also considered for the monitoring of a carbon fiber tubing process.