An uncertainty analysis is required to be carried out in formal safety assessment (FSA) by the International Maritime Organization. The purpose of this article is to introduce the uncertainty analysis technique into the FSA process. Based on the uncertainty identification of input parameters, probability and possibility distributions are used to model the aleatory and epistemic uncertainties, respectively. An approach which combines the Monte Carlo random sampling of probability distribution functions with the a-cuts for fuzzy calculus is proposed to propagate the uncertainties. One output of the FSA process is societal risk (SR), which can be evaluated in the two-dimensional frequency-fatality (FN) diagram. Thus, the confidence-level-based SR is presented to represent the uncertainty of SR in two dimensions. In addition, a method for time window selection is proposed to estimate the magnitude of uncertainties, which is an important aspect of modeling uncertainties. Finally, a case study is carried out on an FSA study on cruise ships. The results show that the uncertainty analysis of SR generates a two-dimensional area for a certain degree of confidence in the FN diagram rather than a single FN curve, which provides more information to authorities to produce effective risk control measures.

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Uncertainty analysis is considered to be a necessary step in the process of vessel traffic risk assessment. The purpose of this study is to propose the uncertainty analysis algorithm which can be used to investigate the reliability of the risk assessment result. Probability and possibility distributions are used to quantify the two types of uncertainty identified in the risk assessment process. In addition, the algorithm for appropriate time window selection is chosen by considering the uncertainty of vessel traffic accident occurrence and the variation trend of the vessel traffic risk caused by maritime rules becoming operative. Vessel traffic accident data from the United Kingdom's marine accident investigation branch are used for the case study. Based on a comparison with the common method of estimating the vessel traffic risk and the algorithm for uncertainty quantification without considering the time window selection, the availability of the proposed algorithms is verified, which can provide guidance for vessel traffic risk management.

The Safety Level Approach (SLA) is a structured application of risk-based methodologies for the International Maritime Organization's (IMO's) rule-making process. When the SLA is applied, safety goals have to be provided. In order to set appropriate levels for safety goals, it is necessary to measure the tolerance degree of the current safety level. Based on the consistency with individual risk criteria and the principle of continuous improvement, this paper proposes an approach to establish the societal risk criteria, which can be used for setting safety goals in the context of the IMO's SLA. Furthermore, by defining dynamic factors to express risk aversion, a method for tolerance measurement of the current societal risk is developed. Finally, a case study into the societal risk evaluation of cruise ships and Roll-On Roll-Off (RO-RO) passenger ships is conducted.