Bathtub-Shaped Failure Rate of Sensors for Distributed Detection and Fusion

We study distributed detection and fusion in sensor networks with bathtub-shaped failure (BSF) rate of the sensors which may or not send data to the Fusion Center (FC). The reliability of semiconductor devices is usually represented by the failure rate curve (called the “bathtub curve”), which can be divided into the three following regions: initial failure period, random failure period, and wear-out failure period. Considering the possibility of the failed sensors which still work but in a bad situation, it is unreasonable to trust the data from these sensors. Based on the above situation, we bring in new characteristics to failed sensors. Each sensor quantizes its local observation into one bit of information which is sent to the FC for overall fusion because of power, communication, and bandwidth constraints. Under this sensor failure model, the Extension Log-likelihood Ratio Test (ELRT) rule is derived. Finally, the ROC curve for this model is presented. The simulation results show that the ELRT rule improves the robust performance of the system, compared with the traditional fusion rule without considering sensor failures.