This paper presents a novel framework called Failure-Alarm Correlation Tree based Failure Localization (FACT-FL), designed to localize failed optical layer device boards in an Optical Transport Network (OTN). Specifically, FACT-FL aims to construct a set of FACTs by correlating the failed boards and alarms, where each FACT takes one failed board and its correlated alarms as the root and leaves, respectively. Furthermore, a FACT consists of a suite of $k^{th}$ order Failure-Alarm Correlation Chains (k-FACCs) with different order values of k. Each k-FACC indicates the chain-like correlation established by k alarms due to one common failed board. To identify all previously undetected k-FACCs, a set of binary classifiers is trained that characterizes each k-FACC from various dimensions, including time, network topology, traffic distribution, and board/alarm attributes. Eventually, an integer linear programming (ILP) problem is formulated to extract the most likely FACT(s) from those k-FACCs. Extensive case studies demonstrate the superior results of FACT-FL in terms of metrics evaluating the identified failed boards and root alarms. We also analyze its performance under different maximum order values of k and environmental changes, including failure scenarios, network topologies, traffic distributions, and noise alarms.