Model-based recursive partitioning (MOB) provides a powerful synthesis between machine-learning inspired recursive partitioning methods and regression models. Hanna Birke extends this approach by allowing in addition for measurement error in covariates, as frequently occurring in biometric (or econometric) studies, for instance, when measuring blood pressure or caloric intake per day. After an introduction into the background, the extended methodology is developed in detail for the Cox model and the Weibull model, carefully implemented in R, and investigated in a comprehensive simulation study.