In order to reduce computation time and cost involved with detecting and diagnosing a fault in a system, simplified representations of components of the system are used to estimate valid intervals for state variables at the components. Generic failure rules are configured to compare the estimated valid intervals to related intervals for the same state variables, from either observations or propagations, for overlap. Failure output vectors are generated based on the comparison, and the failure output vectors are compared to diagnostic matrices to determine a source of the fault.