## 3 Research Results and Discussion
### Exemplary Calculation Results  
**Example 1**. : _Figure 2 presents the graphs of the criterion function, g(x), in the case where g(x) means profit/loss per time (for one technical object [thousand PLN/day]), while, in Figure 3, where g(x) means availability to carry out transport tasks (for one technical object). The following data was used for the calculations:_  
1. _values that come from the matrix of the probabilities of changes in the states of the analyzed model P:_ \[\text{P}=\left[ \begin{array}{cccc}0&0.9080&0&0.0920\\ 0.8093&0&0.1907&0\\ 1&0&0&0\\ 1&0&0&0\end{array} \right]\]
2. _average values of times of the technical object staying in the states of the model in [day]:_ \(ET_{2}\) = 0.21, ET\({}_{3}\) = 0.56, ET\({}_{4}\) = 0.17; for the service life (time to failure), ET\({}_{1}\), the Weibull distribution was adopted, for which the value of the scale parameter scale = 6; three cases were analyzed when the value of the Weibull distribution shape parameter is respectively \(\in\)[5, 7, 9]._
3. _average values of profits (costs) per unit of time in individual states of the model in [thousand PLN/day]:_ \(z_{1}\) = 0.8, \(z_{2}=-3.2\), \(z_{3}=-4.0\), \(z_{4}=-2.1\)_._ _In both cases, for the criterion function, g(x), denoting profit per unit of time (Figure 2) or availability to perform transport tasks as a function of time to preventive replacement (Figure 3), the value of this function is the maximum. For all three considered cases, for each of the examined values of the Weibull distribution shape parameter, the optimal value of time to preventive replacement \(x[h]\) can be calculated. If we examine the values of \(x_{max}\), for which the criterion function g(x) gets the maximum value, we notice that by increasing the value of the shape parameter, the value of \(x_{max}\) increases, but also the maximum value of the criterion function, g(x). The determined values of the Weibull distribution parameters affect the maximum values of the criterion function g(x) and the optimal time of preventive replacement according to age \(x_{max}\)._  
**Example 2**. : _Figure 4 shows the graph of the criterion function where g(x) is the profit per unit of time. Figure 5 shows the graph of the criterion function where g(x) means availability to perform transport tasks. The data from example 1 were used for the calculations. The uptime (time to failure) of ET\({}_{1}\) was assumed to have a Weibull distribution. The parameters for this distribution are: scale = 6 and shape = 9. These plots show four cases:_  
_a--the number of preventive replacements is the same as in Example 1,_  
_b--the number of preventive replacements is increased by 15%,_  
_c--the number of preventive replacements is increased by 30%,_  
_d--when the number of preventive replacements is increased by 45%,_  
_(based on case a)._  
Figure 3: Graphs of the function g(x)—availability to perform transport tasks as a function of time to preventive replacement x [h], determined for a Weibull distribution with parameter values scale = 6 and shape = 5 (curve a), shape = 7 (curve b), shape = 9 (curve c). Figure 2: Graphs of the function g(x)—profit per time unit as a function of time to preventive replacement, x [h], determined for a Weibull distribution with parameter values scale = 6 and shape = 5 (curve a), shape = 7 (curve b), shape = 9 (curve c). Along with the increase in the value of preventive replacements, the value of the criterion function g(x) increases. This is shown in Figures 4 and 5. It happens for profit (loss) over time as well as for availability in the function of transport tasks. The function g(x) has a maximum value for the smaller values of x\({}_{max}\) (optimal value of time to preventive replacement). It follows that, in the transport system under consideration (agricultural tractor operation system), it is possible to increase the efficiency of the technical objects in use as a result of planning additional preventive replacements (increasing the frequency of these replacements).