In this paper, an approach to evaluate the actuator fault tolerance of a nonlinear model predictive control (NMPC) system using viability theory is proposed. Viability theory provides several concepts formulated in a set form (viability kernel and capture basin) that are very useful to assess if after the fault the NMPC controller will be able to achieve their goal either using a reconfiguration or an accommodation strategy. By representing the nonlinear model of the system in a linear parameter varying (LPV) form and using zonotopes to evaluate viability sets, an algorithm is developed and implemented that is able to assess the tolerance of the NMPC controller. To illustrate the proposed approach two application examples based on well-known control problems (a pasteurization plant and a mobile robot) are used. (C) 2018 Elsevier Ltd. All rights reserved.