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Fault detection module is one of the most important components in modern industrial systems. In this paper, we propose a novel fault detection framework which makes use of both normal and faulty measurement signals at the same time. In this framework, the multivariate time series (MTS) pieces which are extracted from measurement signals in a time interval are used as the training and testing samples, and a K-nearest neighbour rule of MTS pieces is applied for fault detection. Moreover, a Mahalanobis distance based dynamic time warping method is used to measure the divergence among MTS pieces, and a one-class metric learning algorithm is proposed to learn the appropriate Mahalanobis distance. Experimental results on the Tennessee Eastman process demonstrate that the proposed method has improved fault detection performance compared with classical approaches on certain kinds of faults.