We consider the problem of placing services in a telecommunication network in the presence of failures. In contrast to existing service placement algorithms that focus on optimizing the quality of service (QoS), we consider the performance of monitoring failures from end-to-end connection states between clients and servers, and investigate service placement algorithms that optimize the monitoring performance subject to QoS constraints. Based on novel performance measures capturing the coverage, the identifiability, and the distinguishability in monitoring failures, we formulate the service placement problem as a set of combinatorial optimizations with these measures as objective functions. In particular, we show that maximizing the distinguishability is equivalent to minimizing the uncertainty in failure localization. We prove that all these optimizations are NP-hard. However, we show that the objectives of coverage and distinguishability have a desirable property that allows them to be approximated to a constant factor by a greedy algorithm. We further show that while the identifiability objective does not have this property, it can be approximated by the maximumdistinguishability placement in the high-identifiability regime. Our evaluations based on real network topologies verify the effectiveness of the proposed algorithms in improving the monitoring performance compared with QoS-based service placement.