While rare events like process drift and damage in ultraprecision manufacturing are not preventable in most cases, the accurate detection could enable timely corrective actions to substantially reduce the severity of the fallout and the associated treatment cost. Nonetheless, subtle process drift in incipient stage generally nullifies conventional data-driven detection algorithms, which are inadequate to track dynamic behavioral evolution for complex systems. Notably, the inevitable sensor failure in conjunction with heterogeneous sensing characteristics have made it strenuous to synchronize data from multiple sources to monitor process variability. To address those challenges, this paper presents a novel intrinsic multiplex graph approach based on intrinsic time-scale decomposition of the signal collected from one single source for the detection of incipient process drift. A case study in ultraprecision machining indicates that this proposed method detects the formation and sweeping away of built-up edge phenomenon with minimal time delay.