where NA is the number of collision candidates and PC is the causation probability, or the probability of a collision candidate becoming a collision (e.g. [36]).
The number of collision candidates (NA) corresponds to the number of collisions if no evasive manoeuvres were made, and it depends on ship traffic properties in the area. The collision candidates can be estimated for a particular crossing of two waterways [42] or using directly Automatic Identification System (AIS) data with the concept of collision diameter defined by Pedersen [42], e.g. as done by Silveira et al. [50].
The causation probability (Pc) can be estimated using two approaches: the scenario approach or the synthesis approach. The scenario approach is used if the causation probability is calculated based on available accident data. The synthesis approach relies on the development of Bayesian Network models to estimate (Pc), i.e. the fraction of collision candidates failing to avoid the collision, which is typically affected by technical, environmental and human factors.
Bayesian Network models have been adapted to causation probability estimation, which vary both in the number and in the nature of their variables. For instance, Friis-Hansen and Simonsen [12] developed a software package called Grounding and Collision Analysis Toolbox (GRACAT), to estimate the probability of vessel collisions and groundings including damage evaluation. GRACAT uses in the calculation of the collision and grounding probabilities the method which is based on the models of Fujii et al. [14] and MacDuff [35]. The BN model for predicting the causation factor for ship–ship collisions was based on the network formulated by Friis-Hansen and Pedersen [11] but extended to model two ships, i.e. ship–ship collision situations. GRACAT software has been used for example in the collision risk estimation of the FSA study performed for the implementation of the VTMIS (Vessel Traffic Management and Information Services) system for the Gulf of Finland.
Another application of BN models for grounding and collision scenarios was undertaken by Norway in conjunction with the FSA on Large Passenger Ships [24]. In this study, risk models were developed for grounding and collision accidents for quantification of Risk Control Options (RCOs), in particular for the evaluation of the effect of ECDIS (Electronic Chart Display and Information System), ENC (Electronic Navigational Charts) and Track control. These BN models for the powered grounding and collision accident scenarios included human factors, technical factors, geographical and other external factors, chosen with the aim to reflect important risk contributors and to be able to evaluate the effect of RCOs. The analysis considered five scenarios that may lead to grounding with probabilities estimated based on expert judgement. Moreover, several factors were considered to influence the ability to perform the navigators' tasks, such as: a) Management factors; b) Working conditions and c) Personal factors that include the physical and mental state of the OOW (fatigue, stress level, intoxicated, etc.). For the collision scenarios, the modelling of loss of control of the vessel is more or less the same as for grounding, except that the interaction with the other vessel (give-way rules and practices, communication, etc.) was included.
Hanninen and Kujala [20] studied the influences of the variables in a Bayesian belief network model for estimating the role of human factors on ship collision probability in the Gulf of Finland. The objectives of this study were to identify the variables with the largest influences and examining the validity of the BN model. The structure of the analysed model was to a large extent based on models presented by DNV [8] and DNV [7]. However, the models of Hanninen and Kujala [20] considered multiple ship types and models both of the encountering vessels. The change in the so-called causation probability (i.e. the fraction of collision candidates failing to avoid the collision, which is affected by technical, environmental, and human factors) was examined while observing each state of the network variables and by utilising sensitivity and mutual information analyses. Changing course in an encounter situation was the most influential variable in the model, followed by variables such as the OOW's action, situation assessment, danger detection, personal condition and incapacitation.
The feasibility of analysing ship accidents by means of Bayesian Networks has been also assessed by Kristiansen [30]. The focus of this study was on powered groundings. The objective was to model the interaction between performance shaping factors and unsafe acts. This BN structure was defined on the basis of a barrier type accident model inspired by Reason's Swiss Cheese model and the HFACS (Human Factors Analysis and Classification System) taxonomy of Shappell and Wiegmann [48] developed for analysis of air transpo