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In this thesis, we estimate the monotonic change point of multivariate Poisson processes using a multi-attribute control chart and maximum likelihood estimator. When a chart signals the presence of a special cause, the process moves to out-of-control state. If we can find an appropriate estimation of change point, searching for the special cause will be easier. We show, when the type of the change is not known a priori, the proposed estimator is an appropriate choice, since it accurately estimates the true time of the process changes, regardless of change type, shift magnitudes and process dimension.