The methodology of auxiliary signal design for robust failure detection based on multi-model formulation of normal and failed systems is used to study the problem of incipient fault detection. Here, the fault is modeled as a drift in a system parameter, and an auxiliary signal is to be designed to enhance the detection of variations in this parameter. It is shown that it is possible to consider the model of the system with a drifted parameter as a second model and use the multi-model framework for designing the auxiliary signal by considering the limiting case as the parameter variation goes to zero. The result can be applied very effectively to early detection problems where small parameter variations should be detected