Shewhart charts are widely accepted as standard tools for monitoring manufacturing processes of univariate, independent “nearly” normal measurements. They are not as well developed beyond these types of data. We generalize the idea of Shewhart charts to cover other types of data commonly encountered in practice. More specifically, we develop some valid control charts for dependent data and for independent data that are not necessarily “nearly” normal. We derive the proposed charts from the moving blocks bootstrap and the standard bootstrap methods. Their constructions are completely nonparametric no distributional assumptions are required. Some simulated as well as real data examples are included they are very supportive of the proposed methods.