Arrearage phenomenon commonly exists in actuators. With arrearages, the actuator cannot achieve the target suggested by the controller, so the control performance degrades. Deadzones and stuck faults can be considered to be two special classes of arrearages, which are studied widely; however, more general arrearage phenomenon cannot be described and treated by these forms. In this paper, a general formulation is introduced for this phenomenon, which is referred as actuator arrearage faults. Based on this formulation, an improved generalized predictive control scheme is proposed for a class of single-input single-output linear systems. With arrearage faults, the system becomes a stochastic process. Hence, a sufficient condition, which guarantees the output tracking error to be uniformly ultimately bounded in the mean-square sense, is presented in this paper. Simulations are given to illustrate the feasibility and effectiveness of the proposed scheme. (C) 2008 Elsevier Ltd. All rights reserved.