## 4 The Research Results
### Selection of the Rank of Downtime Categories and Downtime Periods  
In the next step of the analysis, the dependence of the amount of downtime categorized on downtime category was examined. The non-parametric Spearman method was used. The mean value \(M(UT_{k})\) was adopted as the categorized stoppage value indicator, and the \(V(UT_{k})\) coefficient was adopted as the stoppage category indicator according to Table 3. Taking into account the proportion between the influence of random and deterministic factors, the following ranking of the downtime category was developed:  
1. NB \"current repair\"--category NB includes repetitive maintenance procedures and repeated replacement of wearing parts; therefore, the influence of determined factors is of dominant character, while the influence of random factors is of minority character. In this study, the estimated V(NB) < 0.58 (Table 3). 2. BCZ \"lack of spare parts\"--it is known from company practice that shortages of spare parts are events with a balanced influence of random and deterministic factors. In the study, it was estimated that V(BCZ) = 1.0 +/ - 0.25 (Table 3). 3. ON \"pending repair\"--downtime in this category is related to the awaiting warranty service by the manufacturer, and thus they mainly concern external causes and  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Vehicle’s Make**} & \multicolumn{2}{c}{**Downtime Category**} & \multirow{2}{*}{\(M(UT_{k})\) (\%)} & \multirow{2}{*}{\(Me(UT_{k})\) (\%)} & \multirow{2}{*}{\(SD(UT_{k})\) (\%)} & \multirow{2}{*}{\(V(UT_{k})\)} &  
are difficult to predict and manage. It is known from practice that the influence of random factors (independent of the company's management) is balanced here with the influence of deterministic factors. In the study, the estimated V(ON) = 1.25 +/ - 0.25 (Table 3). 4. NW \"post-accident repair\"--road accidents as the cause of vehicle downtime are random, but it is possible to predict repairs of this category on the basis of statistical data. In the presented research, it was estimated that V(NW) = 1.25 +/ - 0.5 (Table 3). 5. INN \"other causes\"--due to the large number and variety of non-standard causes of downtime, the role of the chance is very large here. In the study, the estimated V(INN) = 1.5 +/ - 0.5 (Table 3). 6. WS \"engine replacement\"--the WS category applies to defects that require removal of the engine, as a result of which the engine is replaced and the damaged vehicle is sent for repair in a separate cycle. It is known from company practice that there is a high uniqueness of downtime duration. In the study, the estimated V(WS) = 4.0 +/ - 4.0 (Table 3). On the basis of the data contained in Table 3, the \(V_{k}\) variation coefficient values characterizing individual categories of stoppages were compiled, the \(x_{k}\) ranks were adjusted, and the Spearman coefficient \(R_{\rm S}\) was calculated. The compilation ranks for the downtime category and the results of the \(R_{\rm S}\) Spearman coefficient calculations are provided in Table 4.  
The obtained result of Spearman's coefficient calculation amounting to R\({}_{\rm s,me}\) = \(-\)0.90 (on average for all bus makes) indicates a negative strong relationship between the category and duration of downtime. In this paper, taking into account the adopted indicators, it means the relationship between the categorized unavailability coefficient (defined as the ratio of the number of coach days of unavailability caused by \(k\)-th cause to the total number of coach days of unavailability covering all causes) and the coefficient of statistical variability as a measure of variation in the tested sample of a given bus brand. The differences in the Spearman's coefficient values between vehicle brands were significant. They were in the range from R\({}_{\rm S}\)(G) = \(-\)0.61 to R\({}_{\rm S}\)(E) = R\({}_{\rm S}\)(C) = R\({}_{\rm S}\)(D) = \(-\)1.00. In the case of low Rs, NB and WS downtimes of extreme ranks stood out.