To plan a rapid response and minimize operational costs, passive optical network operators require to automatically detect and identify faults that may occur in the optical distribution network. In this work, we present DSP-Enhanced OTDR, a novel methodology for remote fault analysis based on conventional optical time-domain reflectometry complemented with reference traces. Together with the mathematical formalism, we derive the detection tests that result to be uniformly most powerful, which are optimal according to the Neyman-Pearson criterion. To identify the type of fault and fully characterize it, the detection stage is followed by the estimation of its characteristic parameters, such as return loss and insertion loss. We experimentally demonstrate that this approach allows to detect faults inside the event dead zone, which overcomes the shortage of conventional event-marking algorithms.