Among the predictive maintenance technologies proposed by many scholars, the exponential-curve-fitting (ECF) model was commonly applied to predict the remaining useful life (RUL) of a target device. However, due to the algorithm’s limitations, when the target device is about to reach its end of life and the target device’s aging feature suddenly rises or becomes smooth, the ECF model may not be able to keep up with the real-time prediction. It may even falsely predict an overly long RUL. To solve the problem of inaccurate RUL prediction, the Time Series Prediction (TSP) algorithm is proposed. TSP applies the time series analysis model built from an information criterion to adapt to the highly complicated task of predicting faults of the target device. Also, the Pre-Alarm Module (PreAM) is introduced to raise an alert of immediate maintenance when a target device is likely to shut down shortly. The Death Correlation Index (DCI) is proposed to reveal the possibility if reaching the target device’s end of life. Real-world data is used to illustrate the TSP algorithm.