This paper proposes a novel scalable model-based fault detection and isolation approach for the monitoring of nonlinear large-scale systems, consisting of a network of interconnected subsystems. The fault diagnosis architecture is designed to automatically manage the possible plug-in of novel subsystems and unplugging of existing ones. The reconfiguration procedure involves only local operations and communication with neighboring subsystems, thus, yielding a distributed and scalable architecture. In particular, the proposed fault diagnosis methodology allows the unplugging of faulty subsystems in order to possibly avoid the propagation of faults in the interconnected large-scale system. Measurement and process uncertainties are characterized in a probabilistic way leading to the computation, at each time-step, of stochastic time-varying detection thresholds with guaranteed false-alarms probability levels. To achieve this goal, we develop a distributed state estimation scheme, using a consensus-like approach for the estimation of variables shared among more than one subsystem; the time-varying consensus weights are designed to allow plug-in and unplugging operations and to minimize the variance of the uncertainty of the fault diagnosis thresholds. Convergence results of the distributed estimation scheme are provided. A novel fault isolation method is then proposed, based on a generalized observer scheme and providing guaranteed error probabilities of the fault exclusion task. Detectability and isolability conditions are provided. Simulation results on a power network model comprising 15 generation areas show the effectiveness of the proposed methodology.