A risk matrix analysis framework is proposed for risk assessment and prioritization based on potential risk influence (PRI). First, a new principle for risk level assignment considers the potential impacts of risk, including controllability, criticality, manageability and uncertainty, is established. Next, the impacts of potential risk are divided into two risk influence factors in risk matrix: probability and consequence influence factor. A fuzzy probability method is used to calculate the failure probability of basic events when appropriate reliability data is unavailable. To take the dependence of basic events into account, Bayesian belief network models established to calculate the likelihood of failure. Finally, to demonstrate the validity of the proposed method, a risk assessment and a risk ranking process are performed for a cryogenic liquid hydrogen filling system (CLHFS). The results of the case study confirmed that the proposed methodology successfully manages risk level inconsistency, and is altogether a feasible and reasonable tool for risk management. (C) 2016 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.