This study introduces an Enhanced Autoregressive Integrated Moving Average (E-ARIMA) model for anomaly detection in time-series data, using vibrations monitored by CA 202 accelerometers at the Kirkuk Gas Power Plant as a case study. The objective is to overcome the limitations of traditional ARIMA models in analyzing the non-linear and dynamic nature of industrial sensory data. The novel proposed methodology includes data preparation through linear interpolation to address dataset gaps, stationarity confirmation via the Augmented Dickey-Fuller Test, and ARIMA model optimization against the Akaike Information Criterion, with a specialized time-series cross-validation technique. The results show that E-ARIMA model has superior performance in anomaly detection compared to conventional Seasonal ARIMA (SARIMA) and Vector Autoregressive models. In this regard, Mean Absolute Error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE) criteria were utilized for this evaluation. Finally, the most important achievement of this research is that the results highlight the enhanced predictive accuracy of the E-ARIMA model, making it a potent tool for industrial applications such as machinery health monitoring, where early detection of anomalies is crucial to prevent costly downtimes and facilitate maintenance planning.