## 1 Introduction  
The European Commission's road map [1] (with a time horizon of 2050) identifies 10 goals in defining transport policy and offers a list of 40 concrete initiatives to achieve the goals. One of them concerns passenger and freight transport, with the following aims:  
* Reducing the share of road transport, with 50% of all medium-distance transport being carried out through rail and water transport;
* By 2030, 30% of freight transport over 300 km should be carried out through rail or water transport, and by 2050, over 50%;
* By 2050, most of the passenger transport over more than 300 km should be carried out through rail transport. The main reasons for the strategic plans formulated in this way are dictated by the huge advantages that rail and water transport have over road and air transport: developed infrastructure, high speed of movement, the possibility of transporting loads of large volume and mass, low cost per unit of work, minimal staff per unit of work, environmental friendliness, high level of safety, and others. In terms of safety (as well as personnel and environmental indicators), rail transport is the undisputed leader among other modes of transport. This stems from the strict regulatory documents for the admission of new vehicles into operation and the regulation of a strict system for operation and maintenance. A special place for guaranteeing accident-free transport is occupied by the wheel-rail interaction. This is the reason why these elements are the subject of a few current studies [2; 3; 4; 5], in which analytical, numerical, and experimental methods related to wheel and rail wear and the derailment phenomenon have been proposed and analyzed. A significant concern in modern publications is the elucidation of the derailment mechanism [6; 7; 8; 9; 10; 11; 12; 13], in which new factors related to the process are introduced. Their reasons are logical since the phenomenon of derailment is a not infrequent event in the modern reality of railway transport and is associated with serious material damage and casualties. Derailments can occur due to the infrastructure or to rolling stock failures as stated in [14]. Some of the publications [8; 9; 11; 15; 16; 17] investigate specific elements (turnouts, guardrails, switches, track defects, lubricators, crossings) or operational indicators (speed, train length, location of wagons carrying dangerous loads) affecting the wheel-rail system and contributing to the derailment of rolling stock. To better investigate the complex phenomenon of derailment, some research activities were devoted to studying the problem from an experimental point of view [18]. Many authors [8; 9; 19] propose the use of numerical methods to theoretically determine the \"safety against derailment\" indicator. In [20], a new type of finite element for FEM analysis is proposed, which more accurately reflects the interaction between the wheel and the rail. The analysis made above clearly shows that there are many theoretically unexplained problems for the occurrence of the derailment process. This is clearly stated in [21], where a critical reading of the currently effective regulatory documents for the admission of new railway vehicles into operation of the European Union, CIS, Great Britain, the USA, China, South Korea, and Japan was made. The authors provide specific explanations of the most common trade-offs, point out the advantages and disadvantages of the methods from the relevant papers, and provide useful recommendations on using simulation methods to assess safety against derailment. The extensive analysis of available publications allows for the determination of the following conclusions:  
* The derailment phenomenon has a distinctly stochastic character. It depends on many factors, which at a certain moment in a complex combination can lead to its occurrence. Current research addresses the issue of derailment from the point of view of theory enrichment by accounting for one or more additional factors that could influence the occurrence of the adverse event.