The realization of early detection of incipient faults makes great sense for the guarantee of system performance and security operation. Therefore, It is necessary to estimate the fault amplitude especially when the system security assessment is the main goal. Regarding the incipient fault with low Fault-Noise-ratio (FNR), in this paper, a practical online fault estimation method is presented for multivariate processes. Statistics based on Kullback-Leibler Divergence (KLD), that is characterized with a high sensitivity to incipient fault, are utilized for the realization of small deviation estimation. Based on the Gaussian assumption, KLDs of different principal components, that characterizes the difference between free-fault and fault case, are computed online through updating the mean and variance of scores. The simulation confirms the feasibility and effectiveness of the proposed incipient fault diagnosis method.