Often when an engineer analyses a system or is supposed to control a system, he uses a mathematical model of the system. In analysis, the engineer can build a descriptive model of the system as a hypothesis of how the system could work, or trying to estimate how an usually unforseeable could affect the system. Similarly, in control of a system the engineer can try out different control approaches in simulations.
Mathematical modelling problems are often classified into white-box or black-box models, according to how much prior information is available of the system. A black-box model is a system of which there is no prior information available, and a white-box model is a system where all necessary infromation is available. Naturally, practically all systems are somewhere between the white-box and black-box models, so this concept only works as a intuitive guide for approach.
Another basic issue is the complexity of a model. If we would, for example, be modelling the flight of an airplane, we could embed each mechanical part of the airplane into our model and would thus acquire an almost white-box model of the system. However, the computational cost of adding such an huge amount of details to the model would effectively inhibit the usage of such a model. Additionally, the uncertainty would increase due to a too complex system, because each separate part induces some amount of variance into the model. It is therefore usually apropiate to make some approximations to reduce the model to a sensible size.
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