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In this study, a fault detection and diagnosis strategy is proposed for the supervision of linearly parametrisable, time-invariant systems subject to abrupt parameter variations, relying on a variation of a set membership identification (SMI) approach. Based on the input-output measurements and the a priori knowledge of the noise bound, the SMI computes a feasible ellipsoidal and its supporting orthotopic parameter set, within which the nominal parameter vector resides. A fault is detected at the time instant when a hyperstrip generated from the measurement data and the noise bound does not intersect with the ellipsoid computed at the previous time instant, or when there is no intersection of the supporting orthotopes. The conditions under which the occurrence of a fault is detected followed by a seamless update of the ellipsoidal set are provided. In the sequel, the fault isolation procedure is accomplished through the computation of the projections of the certainty parameter sets, which contain the new nominal parameter vector. Finally, the fault diagnosis continues with the determination of the size and the type of parameter variation. Simulations studies are used to verify the efficiency of the suggested strategy for the case of multiple faults in a micro-electrostatic actuator.