The Kullback–Leibler (KL) divergence is at the centre of Information Theory and change detection. It is characterized with a high sensitivity to incipient faults that cause unpredictable small changes in the process measurements. This work yields an analytical model based on the KL divergence to estimate the incipient fault magnitude in multivariate processes. In practice, the divergence has no closed form and it must be numerically approximated. In the particular case of incipient fault, the numerical approximation of the divergence causes many false alarms and missed detections because of the slight effect of the incipient fault. In this paper, the ability and relevance to estimate the incipient fault amplitude using the numerical divergence is studied. The divergence is approximated through the calculation of discrete probabilities for faultless and faulty signals. The estimation results that are obtained by simulation induce an error lower than 1% on the fault amplitude.