Low-Density Polyethylene (LDPE) was synthesized from ethylene at high-temperature and pressure condition. Hyper-compressor used to increase pressure up to 3,500 atm should be monitored and controlled delicately or it cannot guarantee stable operation of the process causing process shutdown (SD), which is directly related to product yield and process safety. This paper presents a data-based multivariate statistical monitoring method to detect anomalies in the hyper-compressor of a LDPE manufacturing process with weighted principal component analysis model (WPCA), which can consider both time-varying and time-invariant characteristic of data combining principal component analysis (PCA) and slow feature analysis (SFA). Operation data of the LDPE manufacturing process was gathered hourly for four years. WPCA-based principal component control limit (PCCL) was used as an index to determine anomaly and applied to five emergency shutdown (ESD) cases, respectively. As a result, all the five anomalies were detected by a PCCL, respectively, as a sign of SD. Moreover, it shows a better anomaly detection performance than the monitoring method using T2 and squared prediction error (SPE) based on PCA, SFA, or WPCA.