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The dispersion control charts monitor the variability of a process that may increase or decrease. An increase in dispersion parameter implies deterioration in the process for an assignable cause, while a decrease in dispersion indicates an improvement in the process. Multivariate variability control charts are used to monitor the shifts in the process variance-covariance matrix. Although multivariate EWMA and CUSUM dispersion control charts are designed to detect the small amount of change in the covariance matrix but to gain more efficiency, we have developed a Mixed Multivariate EWMA-CUSUM (MMECD) chart. The proposed MMECD chart is compared with its existing counterparts by using some important performance run length-based properties such as ARL, SDRL, EQL, SEQL, and different quantile of run length distribution. A real application related to carbon fiber tubing process is presented for practical considerations.