## 4 The Research Results
### Descriptive Statistics of AT Availability and UT's Categorized Unavailability  
Using the IBM SPSS Statistics 25 package, a statistical analysis of the \(AT\) availability coefficients distribution and the categorized \(UT_{k}\) unavailability coefficient was performed. In particular, the descriptive statistics were determined: mean value, median, standard \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**No.**} & \multirow{3}{*}{**Vehicle’s Make**} & \multirow{3}{*}{**Manufacturer’s Prestige**} & \multicolumn{3}{c}{**Name of the Indicator**} \\ \cline{3-6}  & & & **Length of the Vehicle (m)** & \
\begin{tabular}{c} **Number of** \\ **the Vehicles** \\ **Tested (pcs)** \\ \end{tabular} &
\begin{tabular}{c} **Average Daily** \\ **Mileage of the** \\ **Vehicle (km)** \\ \end{tabular} \\ \hline
1 & A & Low & 12 & 53 & 201.3 \\
2 & B & Low & 9 & 20 & 151.3 \\
3 & C & High & 18 & 27 & 171.5 \\
4 & D & High & 9 & 10 & 221.8 \\
5 & E & High & 18 & 10 & 217.6 \\
6 & F & High & 12 & 22 & 225.7 \\
7 & G & Medium & 12 & 20 & 226.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the studied bus sample during 12 years of operation. deviation, coefficient of variation, maximum and minimum value. The obtained values of the statistics concerning the availability ratio are presented in Table 2. The frame chart of the \(AT\) availability indicator is presented in Figure 1. A summary of the descriptive statistics for the categorized unavailability coefficient is presented in Table 3. The results of the Shapiro-Wilk test concerning the assessment of the normality of the \(UT_{k}\) variable distribution are also given. The results concerning the availability of buses presented in Figure 1 and in Table 2 show that the average availability over the total research period of 144 months was in the \(AT\approx\) (81.03-92.73%) range depending on the make and model of the vehicle. The highest average availability was achieved by C and F makes, \(M(AT_{C})\) vehicles = 92.73%; \(M(AT_{F})\) = 91.55%). Both brands represented a manufacturer with high prestige. It is also worth noting that the coefficient of variation characterizing the uniqueness of the results had the lowest value here, \(V(AT_{C})\) = 0.05 and \(V(AT_{F})\) = 0.06. The lowest average availability was achieved by vehicles of makes D and B, \(M(AT_{D})\) = 81.03% and \(M(AT_{B})\) = 83.49%. In the literature, the availability of bus communication systems in large urban agglomerations in Poland at the level of 85-90% is assessed as good (satisfactory) in terms of smooth requirements for system (enterprise) functioning. Taking into account all makes and models of the tested buses, the average availability \(M(AT)\) = 87.43% was calculated. This result should be regarded as satisfactory from the point of view of the quality of the vehicle fleet and the effectiveness of the transport enterprise. In the next stage of work, the share of particular categories of downtime in the total period of the vehicles' unavailability of a given make was analyzed. Using Formula (4), the coefficient of unavailability of categorized \(UT_{k}\) was calculated, and then descriptive statistics of this coefficient were determined. The values of these statistics and the Shapiro-Wilk normality test result are given in Table 3. The result of the Shapiro-Wilk test for all the analyzed variables turned out to be statistically significant, which means that their distributions significantly differed from the normal distribution.