Single fault sequential change point problems have become important in modeling for various phenomena in large distributed systems, such as sensor networks. But such systems in many situations present multiple interacting faults. For example, individual sensors in a network may fail and detection is performed by comparing measurements between sensors, resulting in statistical dependency among faults. We present a new formulation for multiple interacting faults in a distributed system. The formulation includes specifications of how individual subsystems composing the large system may fail, the information that can be shared among these subsystems and the interaction pattern between faults. We then specify a new sequential algorithm for detecting these faults. The main feature of the algorithm is that it uses composite stopping rules for a subsystem that depend on the decision of other subsystems. We provide asymptotic false alarm and detection delay analysis for this algorithm in the Bayesian setting and show that under certain conditions the algorithm is optimal. The analysis methodology relies on novel detailed comparison techniques between stopping times. We validate the approach with some simulations.