A typical assumption in supervised fault detection is that abundant historical data are available prior to model learning, where all types of faults have already been observed at least once. This assumption is likely to be violated in practical settings as new fault types can emerge over time. In this paper we study this often overlooked cold start learning problem in data-driven fault detection, where in the beginning only normal operation data are available and faulty operation data become available as the faults occur. We explored how to leverage strengths of unsupervised and supervised approaches to build a model capable of detecting faults even if none are still observed, and of improving over time, as new fault types are observed. The proposed framework was evaluated on the benchmark Tennessee Eastman Process data. The proposed fusion model performed better on both unseen and seen faults than the stand-alone unsupervised and supervised models.