The Cox model is the most popular tool for analyzing time-to-event data. The nonparametric baseline hazard function can be as important as the regression coefficients in practice, especially when prediction is needed. In the context of stochastic process control, we propose a simultaneous monitoring method that combines a multivariate control chart for the regression coefficients and a profile control chart for the cumulative baseline hazard function, that allows for data blocks of possibly different censoring rates and sample sizes. The method can detect changes in either the parametric or the nonparametric part of the Cox model. In simulation studies, the proposed method maintains its size and has substantial power in detecting changes in either part of the Cox model. An application in lymphoma survival analysis in which patients were enrolled by two month intervals in the Surveillance, Epidemiology, and End Results program identifies data blocks with structural model changes.