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In this paper we propose a general framework to compute limiting tolerable hazard rate (LTHR) in complex railway system. The driver machine interface (DMI) is a safety critical component of European Train Control System (ETCS). Functional failure of the DMI can affect the role of the ETCS and can lead to adverse impacts. Therefore, it is important to carry out a careful functional safety analysis of the DMI. The quantification of the LTHR of a DMI is a complex task due to a number of dependencies and uncertainties among event scenarios leading to adverse consequences. Failing to consider dependencies and uncertainties will lead to over or under estimation of the functional safety of a DMI. It motivates the investigation of using Bayesian Networks (BNs) for functional safety analysis of DMI. BNs are acyclic probabilistic graphical model and offer concise representation of dependencies and uncertainties among random variables. The BNs will be used to quantify risk reduction parameters, which will be utilized to quantify LTHR using a mathematical model.