In this paper, we propose a set based approach for detecting faults in input/output channels of a closed-loop multivariable system. This approach works with deterministic bounds on measurement noises, disturbances, and fault signals, which may be attractive in some applications. The fault detection problem is formulated as an optimization problem in the state space framework. The dimensionality of the optimization problem increases with time. In order to allow the problem dimension to be fixed at a pre-specified value, a moving horizon based approach is proposed. When the horizon is moved, a parallelotope covering the feasible region of the initial state is propagated by using the 'Recursive Optimal Bounding Parallelotope' methodology. Diagnosis of the location of a fault is carried out by using a series of detection tests. The usefulness of the algorithm for detection and diagnosis is demonstrated by using a heat exchanger example.