Achieving a safe and lightweight design of composite liquid hydrogen (LH2) vessels without much empirical data requires advanced reliability assessment. An approach based on the Fault Tree method is proposed, to allow the systematization and modelling of functional and structural failure modes and their interactions. A hierarchical system model spanning across the length scales of the LH2 vessel down to the composite material is established. Subsequently, the failure probability of the composite material is estimated in dependence on temperature and load case using Weibull analysis. Using the accident data of US Air Carriers operating under 14 CFR 121 between 2012 and 2019, the probabilities of the load cases are derived, allowing a quantitative reliability analysis of the selected failure modes. Requirements for material and system design are derived in dependence of the maximum allowable failure probability.