This paper discusses the accuracy of different types of models. Statistical models are based on process data and/or observations from lab measurements. This class of models are called black box models. Physical models use physical relationships to describe a process. These are called white box models or first principle models. The third group is sometimes called grey box models, being a combination of black box and white box models. Here we discuss two examples of model types. One is a statistical model where an artificial neural network is used to predict NO_x in the exhaust gases from a boiler at Mälarenergi AB in Västerås, Sweden. The second example is a grey box model of a continuous digester. The digester model includes mass balances, energy balances, chemical reactions and physical geometrical constraints to simulate the real digester. We also propose that a more sophisticated model is not required to increase the accuracy of the predicted measurements.