Although cyclical operation systems are relatively widespread in practice (notably in the realm of physical separations, for example, pressure-swing adsorption and chromatography), the development of specific fault detection mechanisms has received little attention compared to the extensive efforts dedicated to continuous or batch processes. Here, a novel geometric approach for process fault detection is proposed. Specifically, a time-explicit multivariable representation of data collected from the process, which provides a natural framework for defining normal operation and the corresponding confidence regions is developed. On this basis, a two-step fault detection approach is proposed, based on detecting intercycle variations to locate a faulty cycle, and intracycle changes to determine the exact timing of a fault. The theoretical developments are illustrated with two simulation case studies. (c) 2017 American Institute of Chemical Engineers AIChE J, 63: 2719-2730, 2017