Deviation Models Revisited

Tasks like diagnosis, failure-modes-and-effects analysis (FMEA), and therapy proposal involve reasoning about variables and parameters deviating from some reference state. In model-based systems, one tries to capture this kind of inferences by models that describe how such deviations are emerging and propagated through a system. Several techniques and systems have been developed that address this issue, in particular in the area of qualitative modeling. However, to our knowledge, a rigorous mathematical foundation and a “recipe” for how to construct such compositional deviation models has not been presented in the literature, despite the widespread use of the idea and the techniques. In this paper, we briefly revisit the concepts and use of deviation models and related techniques. We reveal (sometimes implicit) presumptions and limitations and present a general mathematical formalization of deviation models. Based on this, aspects of constructing libraries of deviation models, their properties, and their application in consistencybased diagnosis and prediction-based FMEA in a componentoriented framework are analyzed.