When a train repeatedly runs on a track, track irregularities, which are distortions of the track, gradually increase with repetition of wheel load. Tracks are normally inspected periodically so that maintenance can be carried out when a large track irregularities are detected. However, in rare cases, the magnitude of a track irregularity may rapidly increase locally. To ensure the safety of train operations, preventive maintenance is required to detect the signs of such rapid increases in the magnitude of irregularities and to perform maintenance before large irregularities occur. In this study, to identify in advance locations where large track irregularities are likely to occur, we developed a mathematical model that applies cluster analysis to historical data for track irregularities and maintenance records.