The support vector domain description (SVDD) is an efficient kernel method inspired from the SV machine (SVM) by Vapnik. It is commonly used for one-classification problems or novelty detection. The training algorithm solves a constrained convex quadratic programming (QP) problem. This assumes prior dense sampling (offline training) and it requires large memory and enormous amounts of training time. In this paper, we propose a fast SVDD dedicated for multiclassification problems. The proposed classifier deals with stationary as well as nonstationary (NS) data. The principle is based on the dynamic removal/insertion of informations according to adequate rules. To ensure the rapidity of convergence, the algorithm considers in each run a limited frame of samples for the training process. These samples are selected according to some approximations based on Karush–Kuhn–Tucker (KKT) conditions. An additional merge mechanism is proposed to avoid local optima drawbacks and improve performances. The developed method is assessed on some synthetic data to prove its effectiveness. Afterward, it is employed to solve a diagnosis problem and faults detection. We considered for this purpose a real industrial plant consisting in Tennessee Eastman process (TEP).