# Voice Communication Systems Impact on Navigating Officers
## 3 Results  
### Satellite Phone Calls  
For the purpose of this research, a satellite phone call is an incoming call via one of the satellite voice communication systems installed on a navigational bridge. In most cases, these calls are of a business nature from shore-based parties such as a shipping company employee, a cargo owner's company employee, a shipping agent, etc. The conversations are usually rather long and made to exchange voyage plan information, cargo plan or state information, different ship's or crew's issues, etc. Figure 1: The survey questions. In some cases, the OOW could be asked to summon a senior officer (chief officer, chief engineer or the master) on the bridge to take over the conversation. The number of these calls was estimated on the basis of the seafarers' answers in the survey: The seafarers were asked to either state the approximate number of calls during one watch, per day or to state the approximate time between calls. Based on their answers all data were converted to the same expression, which is to the approximate time between calls expressed in minutes. This approach was used for all call types. In the case of satellite calls the dataset showed a significant heterogeneity, whereas a reliable theoretical distribution could not be determined. The collected data (statistical sample) have the following parameters: Range = 1410 min (30-1440 min), Mean = 763.69, Median = 720, Standard deviation = 570.22 and 90% confidence interval for the mean value [656.2, 871.18]. In such cases, knowing the limit values, a uniform distribution with the equal probability within a limited range [a, b] may be used, and is given by the following expressions:  
\[ \begin{split} f(x)=\left\{\begin{array}{l}1/\left(b-a\right) \quad,\ a\leq x\leq b\\ 0\quad\quad\quad\quad,\ \text{\emph{other}}\\ a,b\in R\ ;\ a<b\end{array}\right.\end{split}  \tag{1}\]  
where \(a\) is the minimum limit value and \(b\) is the maximum limit value. The limited range based on survey dataset is [0, 1440] expressed in minutes (Figure 2), thus, the distribution is:  
\[f(t)=\frac{1}{1440-0}=0.694\cdot 10^{-3} \tag{2}\]  
The average time between two consecutive calls may be estimated at one call every 720 min or 12 h, i.e., two per day. To estimate the process time of a satellite call (duration of a conversation) a log file was collected from an LNG carrier in international trade. The collected log file contained 62 incoming calls for the period of 3 months during ship's exploitation. The collected data (statistical sample) have the following parameters: Range = 13.58 min (0.01-13.6 min), Mean = 3.73, Median = 2.39, Standard deviation = 3.51 and 90% confidence interval for the mean value [2.92, 4.54]. The data are congruent with the gamma distribution. Gamma distribution  
Figure 2: Time between two incoming satellite calls [min]. is a continuous asymmetrical distribution, which is for the modelling purposes often used for the description of time duration [20] and is given by the following probability density function:  
\[ \begin{array}{c}f(x)=\left\{\begin{array}{cc}\frac{\beta^{-\alpha}x^{-1}e^{-x /\beta}}{\Gamma(\alpha)}&,\ x>0\\ 0&,\ other\\ \Gamma(\alpha)=\int_{0}^{\infty}t^{\alpha-1}e^{-t}dt\\ \alpha,\beta\in R^{+}\end{array}\right.\end{array}  \tag{3}\]  
where \(\alpha\) is the shape parameter and \(\beta\) is the extent parameter. Therefore, the process times (\(t_{p}\)) of the satellite calls were given in minutes and described by gamma distribution. By rejection of outliners, beyond two standard deviations, the gamma distribution parameters are \(\alpha\) = 1.14 and \(\beta\) = 2.80 (Figure 3):  
\[f\big{(}t_{p}\big{)}=\frac{0.309\cdot t_{p}^{0.14}e^{-t_{p}}}{\Gamma(1.14)} \tag{4}\]  
The average process time (duration of the conversation) of an incoming satellite call is 3.19 min. Considering the frequency of incoming calls and their duration, an OOW spends approximately 6.38 min daily talking on the satellite phone.