  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.
