Two methods are proposed in this article to address distributed data-driven process monitoring. The first method selects sensors and allocates these sensors among subsystems with the objective of optimizing the diagnostic performance of a pattern recognition method when it is implemented in a distributed configuration subject to constraints that are imposed to meet operational requirements. The second method finds the minimum number of monitoring computers required to implement the methods used for fault detection and diagnosis in a distributed configuration subject to certain operational constraints. It also finds the sensors that need to be transmitted to each of the monitors. The proposed methods rely on concepts and algorithms from graph theory and optimization, and their efficiency is shown through a case study on the benchmark Tennessee Eastman Process.