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Survivability is one of the key issues in hybrid wireless-optical broadband access networks (WOBAN) since the single segment failure can cause huge data loss. The single segment failure refers to a scenario where all optical-network-units (ONUs) are disconnected with the optical line terminal (OLT). Previous schemes focus on protecting WOBAN against single segment failure by deploying backup fibers. However, previous schemes suffer from two key problems. First, they ignore optimizing the selection of backup ONUs, which determines the cost of recovering the traffic interrupted by the failure. Second, they underutilize the residual capacity of segments, thus requiring higher backup fibers cost. In this paper, we propose a new and efficient scheme, called Optimizing Backup ONUs selection and backup Fibers deployment (OBOF), to enhance the survivability of WOBAN against the single segment failure. Our OBOF is composed of two consecutive steps, backup ONUs selection and backup fibers deployment. In the first step, aiming to minimize the cost of recovering the traffic interrupted by the failure, the simulated annealing (SA) algorithm is customized to optimize the selection of backup ONUs. In the second step, most importantly, an enhanced greedy cost-efficiency (EGCE) algorithm is proposed to optimize the deployment of backup fibers. Our EGCE consists of a novel remote backup segment (RBS) method, which can efficiently utilize the residual capacity of the segments, and a Bound on Length of Backup-optical-path (BLB) method, which limits the increase in recovery time induced by RBS. Extensive experimental results demonstrate that our OBOF scheme outperforms the previous schemes significantly, especially in the scenario of higher traffic demand.