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Mating a pair of electric connectors is one of the most important steps in a robotic wiring harness assembly system, which can be modeled by static piecewise affine (PWA) systems. To design a fault detection system for this application, a set-membership approach for static PWA systems is proposed, in which parallelotopic approximation of feasible parameter sets is adopted. An online algorithm is obtained to estimate bounds of uncertain transition points of the PWA model. Based on the estimation, a robust online fault detection algorithm is proposed. The robustness and sensitivity of the algorithm are analyzed. The effectiveness of these methods is finally confirmed through experiments.