In response to the demand for higher computational power, the number of computing nodes in high performance computers (HPC) increases rapidly. Exascale HPC systems are expected to arrive by 2020. With drastic increase in the number of HPC system components, it is expected to observe a sudden increase in the number of failures which, consequently, poses a threat to the continuous operation of the HPC systems. Detecting failures as early as possible and, ideally, predicting them, is a necessary step to avoid interruptions in HPC systems operation. Anomaly detection is a well-known general purpose approach for failure detection, in computing systems. The majority of existing methods are designed for specific architectures, require adjustments on the computing systems hardware and software, need excessive information, or pose a threat to users' and systems' privacy. This work proposes a node failure detection mechanism based on a vicinity-based statistical anomaly detection approach using passively collected and anonymized system log entries. Application of the proposed approach on system logs collected over 8 months indicates an anomaly detection precision between 62% to 81%.