The signal issued by a control chart triggers the process professionals to investigate the special cause. Change point methods simplify the efforts to search for and identify the special cause. In this study, using maximum likelihood estimation, a multivariate joint change point estimation procedure for monitoring both location and dispersion simultaneously is proposed. After a signal is generated by the simultaneously used Hotelling's T-2 and/or generalized variance control charts, the procedure starts detecting the time of the change. The performance of the proposed method for several structural changes for the mean vector and covariance matrix is discussed.