In this paper, we propose a decentralized method for maximizing lifetime of data collection wireless sensor networks (WSNs) by making minimal number of nodes operate and putting other nodes in sleep. We divide a target field into multiple grids and make nodes in each grid locally achieve k-coverage. We can reduce energy consumption of WSN by minimizing the number of active nodes required for kcoverage. However, coverage degree is likely to go to excess beyond k near border between grids when deciding active nodes in each grid independently. To solve this problem, our method decides the minimal set of active nodes for adjoined grids at different times so that k-coverage of a grid is achieved taking into account the coverage in its neighboring grids. Through computer simulations, we confirmed that the proposed method achieved distribution of WSN processing with a small decrease of k-coverage lifetime compared to the centralized algorithm.