# Methodology for Studying the Reliability of Interlocking Devices in Bulgarian Railways
## 2 Research Methods
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* interstation devices (IsD)--automatic interlocking without passage signals (AB with axle counters), automatic interlocking with passage signals (type AB with rail circuits), relay semi-automatic interlocking (type PAB), automatic crossing devices (type APU), automatic locomotive signalling (type ALS), points on open road, etc. ;
* telecommunications devices (Tcl)--automatic telephone exchanges (type ATC), external lines, etc. The number and duration of failures by type of equipment and the reasons for their occurrence are specified--due to technical reasons or other causes (thefts, natural disasters, activities of external organisations, etc.). Failure represents the transition from a working state of the device to a non-working state. In principle, a possible failure in one device should not disrupt the proper functioning of the system as a whole. This is why it is necessary to analyse device failures in order to detect components that fail more frequently and to take timely measures to improve their maintenance. Collected data are then summarised in annual consolidated activity reports issued by NRIC (links to publicly archived datasets are provided in the Data Availability Statement Section). In this study, failures of interlocking devices over a period of three years (2020-2022) are analysed and processed according to the following methodology. First, based on the number of failures given in the annual consolidated activity reports, a statistical assessment of devices failures is performed [29]. It starts with calculating the total number of failures of all devices for a given period:  
\[n=\sum_{i=1}^{N}r_{i}(\Delta t), \tag{1}\]  
where \(n\)--total number of failures;  
\(N\)--total number of device types observed in the interval \(\Delta t\) (\(\Delta t\) = 1 year or \(\Delta t\) = 3 years);  
\(r_{i}(\Delta t)\)--number of failures of a specific type of safety devices in the observed interval \(\Delta t\). Then, the percentage ratio by types of devices over the period is calculated using the equation  
\[n_{fi}=\frac{r_{i}(\Delta t)}{n}\times 100,\ \%,\ i=1\ldots\rm{N} \tag{2}\]  
where \(n_{fi}\)--failure rate of the \(ith\) type of safety devices (in a percentage ratio);  
\(r_{i}(\Delta t)\)--number of failures of the \(i^{th}\) device type in the observed interval \(\Delta t\). In a similar way, the total duration of failures of all devices for a given period is calculated (this is the total recovery time):  
\[t=\sum_{i=1}^{N}t_{i}(\Delta t),\ h, \tag{3}\]  
where \(t\)--total duration of failures;  
\(t_{i}(\Delta t)\)--duration of failures of a specific type of safety devices in the observed interval \(\Delta t\). The percentage ratio of the duration of failures by device types for the same period is calculated using the equation:  
\[t_{fi}=\frac{t_{i}(\Delta t)}{t}.100,\ \%,\ i=1\ldots\rm{N} \tag{4}\]  
where \(t_{fi}\)--failure duration percentage of the \(i^{th}\) device type;\(t_{i}(\Delta t)\)--duration of failures (recovery time) of the corresponding device group in the observed interval \(\Delta t\). Using Equations (2) and (4), the percentage of failures and their duration by groups of devices is calculated (for each year 2020, 2021, 2022, and for the three-year period), as well as the percentage for each device type. Second, an analysis of the reliability of the interlocking devices is carried out. In general, reliability is the ability of a device to maintain its basic properties during operation within certain limits. During the analysis, reliability indicators should be determined--they describe the random variables uptime, lifetime, and recovery time [30; 31; 32; 33; 34; 35; 36; 37; 38]. They are usually recorded by the mathematical expectation of the uptime (\(\tau\)), the mean time between failures (\(MTBF\)), and the intensity of the failures flow \(\omega\)(t). The reliability analysis starts with determining simple indicators characterising one property of devices--fault tolerance and repairaability parameters [32; 33; 34; 35; 36; 37; 38; 39; 40; 41].