This paper discusses a distributed diagnosis approach, where each subsystem diagnoser operates independently without a coordinator that combines local results and generates the correct global diagnosis. In addition, the distributed diagnosis algorithm is designed to minimize communication between the subsystems. A Minimal Structurally Overdetermined (MSO) set selection approach is developed as a Binary Integer Linear Programming (BILP) optimization problem for subsystem diagnoser design. For cases, where a complete global model of the system may not be available, we develop a heuristic approach, where individual subsystem diagnosers are designed incrementally, starting with the local system MSOs and progressively extending the local set to include MSOs from the immediate neighbors of the subsystem. The inclusion of additional neighbors continues till the MSO set ensures correct global diagnosis results. A multi-tank system is used to demonstrate and validate the proposed methods.