The paper deals with the problem of active fault diagnosis with deferred decisions for a discrete time stochastic system described using multiple-model framework. The emphasis is placed on reliability of decisions over an infinite time horizon and the admissible lag of a deferred decision is known in advance. The design of the active fault detector with deferred decisions is formulated as a functional optimization problem that is solved hierarchically due to the deferring of decisions. At the top level, the infinite time horizon problem is split into an initial finite time horizon and a terminal infinite time horizon problems that are interconnected at their boundary. The infinite time horizon problem is solved first by using a reformulation to perfect state information problem and subsequent use of approximate dynamic programming. The proposed active fault detector with deferred decisions is illustrated using a numerical example.