# Incorporating Epistemic Uncertainties in Ship Operability Study
## 2 Methods
### Seakeeping Criteria  
Most seakeeping criteria are concerned with operability, i.e., crew ability and willingness to operate a vessel and all its installed equipment in a specified seaway. Operability criteria are typically expressed in terms of roll and pitch angles, roll motion, vertical and lateral acceleration, deck wetness, propeller emergence, and slamming. In addition, there is a group of criteria expressing the interaction between ship motion and human reactions, such as motion sickness incidence and motion-induced interruptions. Limiting values of these criteria are not standardized and do not cover all vessel types, but there are well-established criteria sets referring to the overall vessel system's operability or habitability of the vessel. There are different reasons for discrepancies in criteria between different sources, even if they refer to the similar ship types, such as complexities and inaccuracies of motion prediction methods and discrepancies in the definition of seakeeping amongst naval architects and how vessel owners viewed seakeeping. A critical review of currently used standards and criteria is provided in [32].  
An example of discrepancies of limiting values among different operability standards is given for the case of vertical acceleration at forward perpendicular in [8]. The limiting values read from 0.2 g RMS according to NATO and US Coast Guard Standards, to 0.275 g RMS according to NORDFORSK for Merchant ships less than 100 m in length. There are also other options to express the limiting value of vertical acceleration at the forward perpendicular, such as the probability of exceeding individual acceleration amplitudes and Subjective Magnitude (SM) values [33]. Limiting values for some criteria are less scattered, e.g., limiting value for RMS of the pitch angle of 1.5\({}^{\circ}\) is often found [8].  
The brief review in the preceding paragraph indicates that limiting values are uncertain and that captains could have a different attitude against limiting values for operability criteria. In other words, it is reasonable to consider limiting operability values as random variables. The definition of parameters of probability distributions of such random variables is a challenging task. Performing a questionnaire among experienced seafarers, such as the one presented in [34], could be the right way to define these parameters. The main problem found was the lack of onboard measurements, thus preventing clear quantification of the seakeeping limiting criteria. A large spread among answers to some of the questions, e.g.,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **A** & **B** & **C** & **D** \\ \hline Heave & 0.623 & \(-\)0.000447 & 0.076 & 0.990 \\ Pitch & 0.540 & \(-\)0.000527 & 0.135 & 0.950 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Intercept and regression coefficients for the regression Equation (14).  
estimation of pitch angle, was found. That finding about the uncertainty of operability limiting values supports the necessity of their probabilistic description, as proposed in the present study.  
For illustration of the procedure, the mean values of the operability limiting value are taken from those given in Table 2, while their coefficient of variation (CoV) is assumed as 0.05 in all cases. Gaussian distribution is used to model this uncertainty.