In rotating machinery condition monitoring, traditional health indicators (HI), including quantitative and dimensionless forms, are widely used for health assessment. However, such indicators often respond slowly to early faults or display decreasing and oscillatory trends after fault onset, causing delayed monitoring and economic losses. To address these issues, this study proposes a novel HI termed the time-weighted fusion waveform factor (T2WF). Derived from the conventional waveform factor (WF), T2WF introduces the concept of periods, computes dimensionless values in proximal and distal periods, and combines them through a weighting parameter. The Northern Goshawk Optimization Algorithm (NGOA) is employed to optimize the key parameters. Validation is conducted on the public XJTU-SY dataset and on rotating machinery datasets from two petrochemical enterprises. Experimental results show that T2WF achieves earlier fault detection and superior diagnostic performance compared with traditional HI, international standards, and deep learning methods.