The paper presents a new design for a robust output observer and demonstrates that it can be used to detect sensor faults in uncertain systems with output disturbances. The time-domain design uses an I-infinity technique to minimize a norm of the estimation error. The estimation error forms a residual signal that is the basis for fault detection, fault isolation and disturbance rejection. The minimum detectable fault and the maximum non-detectable fault are introduced to quantify the sensitivity of the detection scheme at a given alarm threshold. These quantities are obtained as solutions to non-convex optimization problems.