The paper shows how a fault diagnosis algorithm based on stochastic automata as qualitative models can be improved by tensor decomposition methods to make it applicable to complex discrete-time systems. While exponential growth of the number of transitions of the automaton with the number of states, inputs and outputs of the system can in principle not be avoided, matrix representations of the automaton can be reduced by exploiting the underlying tensor structure of the behaviour relation. For non-negative CP tensor decomposition, algorithms are available that can be tuned by defining an order of the approximation. The example of a heat exchanger shows the applicability of the proposed method in situations where real measurement data of the nominal behaviour are available and the modelling effort has to be small.