Fault detection and isolation in dynamic systems rises decision problems in the presence of nuisance parameters (unknown initial states, unknown inputs, uncertain parameters). The strict decoupling strategy proposed in control approaches may sometimes fail to be applicable, while statistical decision rules can only be proven to be asymptotically optimal under special assumptions on the faults. In this note, a game-theoretic problem formulation, which is not purely geometrical. and not purely statistical, is proposed and solutions are characterized under some reasonable assumptions.