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Network lifetime is a critical concern in the design of wireless sensor networks. Though many different definitions of network lifetime have been used in the literature, we introduce a function-based network lifetime definition, which focuses on whether the network can perform a given task instead of whether any individual sensor is dead. Then we derive an upper bound of function-based network lifetime for estimation, and we maximize it by introducing a concept of equivalent unit-resource mean square error (MSE) function. The proposed algorithm is optimal and the simulation results show that a significant gain is achieved by the proposed algorithm compared with heuristic methods.