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A local algorithm is proposed and analyzed to monitor the healthiness of a wireless sensor network. Using this local algorithm, we can detect the defective sensors inside the network. The robustness of this algorithm is gauged using the breakdown ratio. We show that for the proposed algorithm, the breakdown ratio can be simply found by solving a quadratic equation. Since the number of defective nodes in a wireless sensor network is assumed to be small compared to the total number of nodes, the compressed sensing algorithm is used to detect the defective nodes also in the fusion center with a low communication cost. The simulation results show that the defective nodes can be successfully detected inside the network and in the fusion center with a low communication cost.