This paper deals with fault detection methods taking model uncertainties into account. It focuses on static and structured uncertain models where parameter uncertainties are described by bounded variables. In order to search the minimal subset of constraints which allow to eliminate all the unknown variables to establish an analytical redundancy relation (ARR) afterwards, one method is proposed in this paper based on the graph path search. And to avoid constructing and evaluating the final ARR by hand, the second part of our algorithm proposes to use the combination of constraint satisfaction problem for solving ARRs and interval analysis for treating model uncertainties