In this paper, a new multi-attribute control chart is initially proposed to monitor multi-attribute processes based on a transformation technique. Then, the maximum likelihood estimator of a multivariate Poisson process change-point is derived for unknown changes that are assumed to belong to a family of monotonic changes. Using extensive simulation experiments, the performance of the proposed change-point estimator is compared to the ones derived for step-changes and linear-trend disturbances, when the true change types are step-change, linear trends, and multiple step changes. 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.