The design of fault detectors for fault detection and isolation (FDI) in dynamic systems is considered in this paper from a norm based point of view. An analysis of norm based threshold selection is given based on different formulations of FDI problems. Both the nominal FDI problem as well as the uncertain FDI problem will be considered. With reference to this analysis, a performance index based on norms of the involved transfer functions is given. A method for designing FDI filters which will minimize the performance index is also given.