Decentralized sequential change detection with ordered CUSUMs

We consider the problem of decentralized sequential change detection, in which K sensors monitor a system in real time, and at some unknown time there is an anomaly in the environment that changes the distribution of the observations in all sensors. The sensors communicate with a fusion center that is responsible for quickly detecting the change, while controlling the false alarm rate. We focus on two families of decentralized detection rules with minimal communication requirements. First, we assume that each sensor runs a local CUSUM algorithm and communicates with the fusion center only once, when it detects the change. The fusion center then declares that a change has occurred when m of the K sensors have raised an alarm. Assuming that all sensors have the same signal strength, we show that the asymptotic performance of these one-shot schemes is free of m to a first order, but decreases with m to a second-order, suggesting that the best strategy for the fusion center is to detect the change with the first alarm. Second, we consider schemes that detect the change when m of the K sensors agree simultaneously that the change has occurred. While a first-order asymptotic analysis suggests that it is optimal for the fusion center to wait for all sensors to agree simultaneously, a second-order analysis reveals that it can be better to wait fewer (but more than half) of the sensors to agree. The insights from these asymptotic results are supported by a simulation study.