Incipient fault diagnosis is an important and challenging issue in academic and industrial communities but got insufficient attention. Recently, the local Mahalanobis distance was proposed and applied to incipient fault detection, which is shown to be effective for non-linear data and sensitive to incipient faults. However, this method's performance degenerates when training samples contain outliers. To cope with this issue, we propose robust healthy domain approximation based on a specific anchors-generating algorithm to improve the local Mahalanobis distance calculation. Simulation results show that the new proposed anchors-generating algorithm can significantly avoid the interference caused by outliers and then develop a performed healthy domain approximation for a more accurate fault detection procedure. The comparison result between our proposal and other one-class classification methods highlights the efficiency of the proposed solution for incipient fault detection.