Effective monitoring of chemical processes is required to ensure safe and economical operation. Data-driven monitoring methods are popular for detecting and diagnosing faults in chemical plants. An effective approach for implementing a data-driven monitoring method to detect and diagnose faults in large-scale systems such as chemical plants is to do so in a distributed configuration. A decomposition (i.e. an allocation of sensors among different sets called subsystems) must be selected before a monitoring method can be implemented in the distributed configuration. The monitoring method is then applied to each subsystem to come to a local decision as to whether a fault is detected or what the local diagnosis is. Finally, a consensus strategy uses the local decisions of the subsystems to reach a final fault decision. The performance of a fault detection method can be improved when it is implemented in the distributed configuration. Some of the operational constraints associated with implementing a monitoring method for a large-scale system can also be satisfied in the distributed configuration. For example, distributed methods can be implemented using computers installed at multiple locations if transmitting measurements from all the sensors to a single location is difficult. The ability of the distributed configuration to satisfy operational constraints and the performance of the distributed methods depend on the selected decomposition. The first objective is to propose methods which find a decomposition for which the performance of a distributed data-driven monitoring method in detecting or diagnosing a set of faults is near optimal subject to user-imposed constraints. The proposed methods use greedy search algorithms to generate many feasible candidate decompositions and subsystems and then use process data to directly evaluate the performance of these candidates to find a near optimal decomposition. The second objective is to propose methods which find the minimum number of locations required for distributed monitoring and the monitoring tasks that should be implemented at each location subject to user-imposed constraints. A commonality in the proposed methods is that they use algorithms from graph theory. The proposed methods are also fully automated and software for the methods is made available.