## 5 Characteristics of a Tested Object--Station System
Available checks, i.e., such that can be implemented at a given signal box post, are defined based on the track system, list of routes and available commands. This requires converting a locking sheet into a sheet showing routes, but which contains elements written using control and monitoring algorithms. The sheet can be supplemented with available station documentation, post-operation rules and a schematic plan, e.g., defined indications on the signalling devices depending on the ABS type or variant movements. For the track system shown in Figure 2, the task sheet, a modified locking sheet containing tested control and monitoring algorithms, is shown in Figure 3. The sheet contains a column with task execution cost, route identifier and description, as well as sections with such route elements as the section with points Z and their numbers, a section with signals/indications S, and a section with track/points sections with section names. Figure 3: \(Cont.\)  
To improve the legibility of the Figure 3 sheet, the fragment below which contains a points section for entry routes from under signals A and B is presented. where (Figure 4):  
* C--generalized task execution cost (e.g., 3 for route A1);
* A1, A11--No. of route to track 1;
* A2, A21--No. of route to track 2;
* bz--variant without stopping (requires operating wayside equipment and setting the route to exit from the station; hence, the cost is higher than in a similar route on the same track (A1, A11);
* 1, 2, 3,... 8--points number;
* a11--points section--algorithm of points 1 executing + points setting;
* a12--points section--algorithm of points 1 executing \(-\) points setting;
* \"1\" in a cell corresponds to an algorithm used within a task;  
Figure 3: Locking sheet in the notation of control and monitoring algorithms. * An empty cell means that an algorithm is not used in the task/tasks. A sheet constructed this way shows all possible checks that can be executed within the said signal box post. Empty cells in the sheet mean that a given algorithm remains unused, and a zero is inserted in the mathematical model. Determining the check objective allows us to narrow down the set of tests for a specific element or an entire application already at this stage by removing appropriate untested configuration elements. The check sheet (Figure 3) can be presented as a matrix of variables \(x_{i,j}\) \(\in\) {0,1}. These are the coordinates of individual algorithm cells in sections. \[ \begin{array}{l}x_{11}x_{12}x_{13}\ldots x_{1j}\\ x_{21}x_{22}x_{23}\ldots x_{2j}\\ x_{31}x_{32}x_{33}\ldots x_{3j}\\ \ldots\\ x_{i1}x_{i2}x_{i3}\ldots x_{ij}\end{array}  \tag{1}\]  
(for example, \(x_{13}\) to the cell with algorithm a21 for points 2 in the A1 route to track 1) and the task execution cost matrix \(c_{i}\) \(\in\) {1,n}:  
\[c_{1}c_{2}c_{3}\ldots c_{n} \tag{2}\]  
Accordingly, the cost \(c_{1}\) is the execution cost for task A1, \(c_{2}\) is the execution cost for task A11. The algorithm employs the following conditions:  
* Checking each control and monitoring algorithm at least once. This is important from the perspective of determining system fitness state or availability. To have complete information on the tested object requires checking all functions implemented by the system. The condition involves monitoring columns that contain the studied algorithms within the task sheet:  
\[ \begin{array}{l}x_{11}+x_{21}+x_{31}+\ldots+x_{i1}\geq 1\\ x_{12}+x_{22}+x_{32}+\ldots+x_{i2}\geq 1\\ x_{13}+x_{23}+x_{33}+\ldots+x_{i3}\geq 1\\ \ldots\\ x_{1j}+x_{2j}+x_{3j}+\ldots+x_{ij}\geq 1\end{array}  \tag{3}\]  
Figure 4: Locking sheet in the notation of control and monitoring algorithms (a points section for entry routes from under signals A and B). * Not every check must be used There is no need during testing for all available checks to be applied. Each check contains a few algorithms, whether partially or fully overlapping, that occur within different checks.