# Incorporating Epistemic Uncertainties in Ship Operability Study
## 1 Introduction  
The prediction of the seakeeping behavior of ships for a variety of probable environmental and operational conditions has wide application in the shipping industry, providing important information about the design and efficient/safe operation of modern ships. For a ship sailing in waves, the basic controllable parameters are the forward speed and the heading to the waves, so the ship operability study aims to determine in which sea states, described by a significant wave height (\(H_{S}\)) and peak spectral periods (\(Tp\)), the ship can maintain a given course and speed. In ship design, ship operability studies could be utilized to determine the operability index (OI), which represents basically the proportion of time a ship is accessible for perfect operation [1]. The OI considers simultaneously the wave characteristics of the sailing area, the dynamic ship response to the waves, and the ship mission. The ship OI may be used as a decision-making tool when acquiring a new ship for a specific service, to compare the comfort level of different ships [2], and for ship form optimization [3]. There are variations of the OI, such as the operability robustness index (ORI), a performance criterion used to assess the robustness of a vessel in different sea states [4]. The Habitability Index (HI) refers to the assessment of onboard comfort and livability, particularly for passenger vessels [5]. The Comfort Index (CI) is used to assess passenger comfort aboard vessels,especially on longer journeys. This index considers factors like motion sickness, noise levels, and vibrations, using probabilistic methods to predict comfort levels under various sea conditions. It allows operators to anticipate discomfort and optimize routes to minimize passenger distress [6]. In ship operations, operability studies are used for real-time decisions in Decision Support Systems (DSS), where the time frame may be hours (tactical decisions) or days (strategic decisions relating to route planning) [7]. Tactical decisions are made at the navigation bridge, related to the choice of ship speed and course having an impact on the ship motions and loads due to the wave action. In that respect, the following commands could be given: no change is required, speed reduction, course change, or speed and course change [8]. The strategic decision is to determine, before the mission, which route the ship may take, duly accounting for structural safety, the total travel time, fuel consumption, etc. A strategic decision about ship routing is, therefore, a multi-attribute decision-making process [9]. Examples of operational decision-making include predicting first-order vessel responses as a key component of decision support systems, examining the effects of uncertainties in sea state descriptions on operational limits, and presenting a new model for adaptive weather routing based on seakeeping analysis and optimization, aimed at reducing operational risks [10; 11; 12]. Operability analysis as a part of weather routing is presented in [13]. In the common ship operability studies, the seakeeping calculations and assessments are based on specific ship-inherent and environmental data and assumptions. Thus, seakeeping tools are employed assuming their results as ground truth, while seakeeping limiting values are also considered as fixed, prescribed values. However, different seakeeping theories may result in rather different outcomes of the operability studies [14]. The uncertainties associated with the sea state descriptions used in the numerical analysis influence the operational limits (in terms of \(H_{S}\) and _Tp_) [11]. The effect of the seakeeping criteria on the seakeeping performance assessment for passenger vessels shows that the OI is strongly affected by the chosen limiting values [15].