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This paper analyzes the problem of distributed detection in a sensor network of binary sensors. In particular, statistical dependence between local decisions (at binary sensors) is assumed, and two complementary methods to save energy have been considered: censoring, to avoid some transmissions from sensors to fusion center, and a sleep and wake up random schedule at local sensors. The effect of possible failures in transmission has been also included, considering the probability of having a successful transmission from a sensor to the fusion center. In this scenario, the necessary statistical information has been identified, the optimal decision rule at the fusion center has been obtained, and some examples have been used to analyze the effect of statistical dependence in a simple network with two sensors. (C) 2016 Elsevier B.V. All rights reserved.