Predictive maintenance is one of the main approaches which Industry 4.0 is based on, since it aims at reducing unplanned downtime and maintenance costs of industrial machines. In this work, a time-aware clustering-based approach to the analysis of sensor data is presented for the purpose of monitoring the time evolution of the health status of an industrial machine. A possible application of the proposed framework to predictive maintenance is then proposed. As a relevant representative application scenario, the focus is on one of the key machines in a pharmaceutical plant: a freeze-dryer. The illustrated procedure allows to carry out a time segmentation of the properly sensed data. More precisely, the corresponding operational points (associated with features of the sensed data) are clustered using various algorithms, among which Density-Based Spatial Clustering of Applications with Noise (DBSCAN) turns out to be the best. The benefits of the proposed approach are (i) its general nature and (ii) the limited amount of needed features that have to be extracted from a single sensor signal. The proposed procedure is attractive when the collected data (e.g., from a single sensor) are not sufficient to build an accurate physical model of the monitored component.