## 4 Re-Designing of the Appropriate Fairway Width
### Assessment Overview  
Various models are used to evaluate the risk of collision and grounding. In this study, the ES model was used for the collision risk and the IALA MkII model was used for the grounding risk model. The risk model related to maritime traffic and operation can be separated into a traffic status evaluation model, a navigation difficulty evaluation model, and an IALA evaluation model. The evaluation model can be applied according to the variables of each element, and, as in this study, it is appropriate to apply the navigation difficulty evaluation model to analyze the psychological effect of the fairway width on the operator. Operational difficulty evaluation models include the SJ model, BC model, ES model, PARK model, and other models [37]. Among them, the ES model is a model that quantitatively expresses the traffic situation of nearby ships and the degree of risk for navigation obstacles. In the Maritime Traffic Safety Assessment, changes in the maritime traffic environment due to new fairways and facility construction are evaluated using the ES model. Therefore, in this study, collision risk was evaluated using the ES model. The evaluation related vessel grounding was first proposed in the 1980s, and different models are applied depending on the research purpose and variables. [PERSON] and [PERSON] (2010) divided the grounding risk assessment model into two groups: an analytical model and a statistical model. The analytical model includes [PERSON]'s model and [PERSON]'s model, and the statistical model includes the Pedersen Mmodel and Simonsen Model. Among them, the [PERSON] and Simonsen models have been the most used recently and are the basis of the current IWRAP MkII of IALA. Although it is difficult to say that a specific model provides more accurate results than other models, in previous studies, [PERSON]'s model and [PERSON]'s Mmodel were suggested to have weaknesses in probability analysis, and the [PERSON] model was evaluated to be more reasonable than the Pedersen Model [38]. Therefore, in this study, IWRAP MkII, to which the statistical model was applied, was used as a grounding risk analysis model. In this chapter, the concept and theoretical background of the ES model, used to evaluate the collision risk of a ship, and the concept and theoretical background of the IWRAP Mk II model, to evaluate the frequency and probability of a ship's grounding, are reviewed. Furthermore, to ensure the reliability of the evaluation, an evaluation scenario was established and presented. 1. ES Model  
The environmental stress (ES) model was developed to classify the marine traffic environment surrounding a ship into an operating environment and the sea area environment, and to quantitatively evaluate the degree of stress applied to the ship operator by these two environments. The ES model considers the bearing and distance to obstacles and the speed between ships in the range of \(\pm 90^{\circ}\) centering on the course of the ship, calculates the time margin, and quantifies the time margin as a stress value felt by the ship operator. The amount of environmental stress that a ship operator experiences is called the ES value. The environmental stress value consists of an ES value for land (\(ES_{L}\)), which is the amount of stress caused by the marine environment, such as topography or facilities, and the ES value for ships (\(ES_{S}\)), which is the amount of stress caused by the operating environment, such as other ships. The stress values are aggregated and called the aggregation of ES (\(ES_{A}\)) values. The ES stress is classified into four levels (0-500, 500-750, 750-900, and 900-1000). If the stress level is 750 or more, it is evaluated as an acceptable limit, and if it is 900 or more, it is evaluated as unacceptable [37; 39; 40]. In this study, the \(ES_{A}\) value was used to evaluate the risk of collision between ships passing a fairway and the risk due to the operation of the ship within a limited fairway. First, the \(ES_{L}\) calculation method is given in Equations (5) and (6) [37].