## 5 Results
### The Trend in Annual MTTF  
Based on the operational data collected, MTTF\({}_{\text{D}}\) values were calculated from Equation (1), by year, for the selected equipment in the following years. The number of hours  
Figure 4: Waiting time intervals for spare parts in case of replacement.  
Figure 3: Classification of damage according to the method of repair.  
Figure 2: Classification of damage according to the time taken to repair it.  
between failures is presented in Figure 5. It can be observed that the longest time between failures is for the years 2012, 2019, 2012, and 2018, respectively, for technical objects, unit 1, unit 2, and unit 3.  
The characteristic evolution of the annual values of the MTTF\({}_{\mathrm{D}}\) indicator was observed, where it was possible to observe a trend in the change of the indicator value. By plotting the trend line, it is possible to estimate the direction of change (increasing or decreasing) and the approximate value of the indicator in the planning year. To confirm the correctness of the assumptions, an estimation of the MTTF indicator was performed based on selected probability distributions. The estimation of the selected parameters of the individual distributions was performed with the Weibull++ software 11.1.1 [28], using flight data from the maintenance support information system.  
The study's results are presented figuratively in the following forms: Figures 6a, 7a and 8a display the reliability function R(t), with the blue line indicating the average value of the function, and the red lines representing the two-sided limits of the 90% confidence interval. Figures 6b, 7b and 8b illustrate the probability density function f(t), which shows the distribution of data over time. Finally, Figures 6c, 7c and 8c show the histogram, which rearranges the abundance of damage in qualified time intervals or the consumption of residual life (FH, number of landings, cycles, etc.).  
Figure 5: Trend of change in annual MTTF\({}_{\mathrm{D}}\) over 2012–2019 for selected equipment built on a training helicopter.  
Figure 6: (**a**) Reliability function, (**b**) probability density function, (**c**) histogram for Unit 1.  
Figure 7: (**a**) Reliability function, (**b**) probability density function, (**c**) histogram for Unit 2.  
The other distributions used showed less graphic fit, but the numerical values are very similar. Only the value of the estimated MTT factor using the lognormal distribution differs slightly from the other distributions and especially from the MTT\({}_{\text{D}}\) value calculated from Formula (1).  
The numerical data of the MTT\({}_{\text{D}}\) indices are summarized in Table 2.  
The data presented in Table 2 show that using the MTT\({}_{\text{D}}\) factor based on Formula (1) is legitimate, which is proven by the similar values of the factors estimated from the statistical distributions. Because the training helicopter, by definition, has to fly 300 h per year, the differences in the MTT\({}_{\text{D}}\) and MTTF values determined from the distributions are small and can be considered negligible.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Unit**} & \multirow{2}{*}{**MTTFD**} & \multicolumn{4}{c}{**Type of Distribution—MTTF**} \\ \cline{3-5}  & & **Weibull 2 p** & **Lognormal** & \multicolumn{2}{c}{**1 p— Exponential**} & **Normal** \\ \hline
1 & 296 & 446 & 584 & 407 & 407 \\
2 & 890 & 872 & 880 & 874 & 874 \\
3 & 207 & 218 & 275 & 229 & 229 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The comparison of experimental MTT\({}_{\text{D}}\) with MTTF estimated from the chosen probability distributions.  
Figure 8: (**a**) Reliability function, (**b**) probability density function, (**c**) histogram for Unit 3.