In this paper, the problem of identification for passive robust fault detection, when a bounded description of the modelling uncertainty is considered, is addressed. Two set-membership identification methods are introduced to address this problem: the interval predictor and bounded error approaches. These two identification approaches naturally lead to two robust fault detection tests: the direct and inverse tests, respectively, which are also introduced and discussed. Implementation algorithms make use of a zonotope to approximate the parameter uncertainty set. Moreover, underlying hypothesis of both approaches is discussed and applicability conditions are stated. A case study based on a four-tank system is used to illustrate the applicability and the properties of the two identification approaches as well as the corresponding fault detection