# Factors Influencing the Action Point of the Collision Avoidance Manoeuvre
## 3 Results  
### Stage I  
#### 3.1.1 Distance between Ships at the Start of the Manoeuvre  
The first parameter examined was the distance between the ships at the time of making the decision to start the manoeuvre. Calculations were initially carried out for all situations and then separately for open and restricted sea areas. The results are presented in Table 2.  
The distributions of the distance between the ships at the start of the manoeuvre are shown in the histograms (Figure 1).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Value** & **All Situations** & **Open Sea** & **Restricted Sea** \\ \hline Mean & 9.4 NM & 10.3 NM & 7.6 NM \\ Standard deviation & 4.4 NM & 4.5 NM & 3.7 NM \\ Min & 2.7 NM & 3.5 NM & 2.7 NM \\ Max & 19.8 NM & 19.8 NM & 14.8 NM \\ Range & 17.1 NM & 16.3 NM & 12.1 NM \\ S-W \(p\)-value & 0.0295 & 0.16 & 0.14 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Basic statistics for the distance between ships at the start of the manoeuvre.  
3.1.2. Time to CPA (TCPA) at the Start of the Manoeuvre  
On the basis of the gathered data, basic statistics on the TCPA at the start of the manoeuvre were calculated. As for the distance between ships, all situations were initially analysed, regardless of the type of area, then for the open and restricted sea areas separately. The obtained results are presented in the Table 4.  
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**Distribution** & \multicolumn{3}{c}{**All Situations**} & \multicolumn{3}{c}{**Open Sea Area**} & \multicolumn{3}{c}{**Restricted Sea Are**} \\ \hline  & & & & & & & & & & \\  & & & & & & & & & & \\  & & & & & & & & & & \\  & & & & & &  
The Shapiro-Wilk test did not confirm the normality of the distribution (\(p\)-value \(<0.05\)) for all situations analysed together, while for the situations divided according to the type of area, it confirmed the normality of the distributions. This is mainly due to the differences in the manoeuvring methods in different water areas.  
The results of fitting selected theoretical distributions are presented in Table 3. The best fitted distributions are presented in Figure 1. The results show that for all situations analysed together and for the situations in restricted sea areas, the Weibull distribution is the best fitted to the obtained measurements. For the situations in the open sea areas, the results indicate that according to the K-S test, the best fitted theoretical distributions are normal and Weibull, while the chi-squared test indicates the Rayleigh distribution.  
The distributions of the TCPA at the start of the manoeuvre are shown in the histograms (Figure 2).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Value** & **All Situations** & **Open Sea** & **Restricted Sea** \\ \hline Mean & 26.7 min & 30.1 min & 19.7 min \\ Standard deviation & 14.0 min & 14.9 min & 8.3 min \\ Min & 5.5 min & 13.2 min & 5.5 min \\ Max & 82 min & 82 min & 39 min \\ Range & 76.5 min & 68.8 min & 33.5 min \\ S-W \(p\)-value & 0.00002 & 0.0002 & 0.481 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Basic statistics for the TCPA at the start of the manoeuvre.  
Figure 2: Histograms of the TCPA at the start of the anti-collision manoeuvre and the best fitted theoretical distributions for all situations (**a**) in the open sea area (**b**) and in the restricted sea area (**c**).  
Despite the fact that the Shapiro-Wilk test confirmed the normality of the distribution for the restricted sea area, the shape of the histogram and the results for all situations and for open sea areas suggest consideration of other theoretical distributions (e.g., log-normal). The results of fitting selected theoretical distributions are presented in Table 5.  
The results show that for all situations analysed together and for the open sea area, the log-normal distribution is the theoretical distribution best fitted to the obtained measurements. For the restricted area the best fitted distribution is Weibull.