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.

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.

The uncertainty analysis has been conceived as a necessary step in the engineering research in various fields. The purpose of this article is to introduce the uncertainty analysis technique into the process of statistical modelling. Based on the theory of fuzzy random variables, aleatory and epistemic uncertainties in the statistical modelling process can be modeled by fuzzy random variables, which are interpreted as random variables with fuzzy statistical properties. An important aspect of modelling uncertainties lies in the appropriate selection of time window, which is used for the inclusion of data. In order to avoid the arbitrary choice of time window, a simple method for time window selection is proposed by analyzing the uncertainty and the stability of statistic data. Finally, a case study is carried out on the accident statistics. The results show that the proposed methods are effective and can provide more information for decision-making.