The sustainability of services in undertakings which operate in railway passenger transport is closely connected with efforts to provide high-quality and time-acceptable services to the customer, to achieve lean processes, to standardise work processes, to eliminate wastage and to avoid those activities which do not add any value. Considering its ecological nature and big volume of passenger transport, railway passenger transport represents an irreplaceable sustainable system for the future. These facts and the entry of new railway carriers into this system highlight the importance of managing risks in a progressive way. This article focuses on the options of risk management when versatile and flexible tools, such as Lean tools, are set correctly. The aim of this article is to introduce a proposal for the application and a specific application of Lean philosophy in risk management which impacts train delays in railway passenger transport. From the point of view of quantitative data analysis, multiple mathematical-statistical tests have been used to assess data (e.g., Anderson–Darling test, Kolmogorov–Smirnov test, Jarque–Bera test, two-tailed test, Grubbs’s test and Thompson Tau test). Also, descriptive statistics and ANOVA test (Analysis of Variance) have been applied in the process of evaluating the monitored attributes. In order to assess the data dependency, Chi-Square Test and a correlation analysis have been applied. The research outcomes focus on highlighting the need for a systematic approach for train delays and to avoid delays through risk management. The case study applies selected Lean methods to monitor train delays in selected stations within the main railway corridor of the Slovak Republic for the period from 2015 to 2018. In 2019, the results were processed and created a basis for proposing a unique software tool like an aid for risk management in the case of train delays using Lean philosophy. The flexible software includes the participation of employees, and at the same time, it respects the needs of customers. The research results provide grounds for further study of risks in a challenging environment of railway undertakings, with different types of trains, railway stations as well as entire railway networks. The processed results of the article represent valuable material for railway undertakings not only in Slovakia but also for railway organisations in V4 countries.

Nowadays, it is essential to contribute to sustainable transport to the maximum extent possible. Therefore, a significant emphasis is placed on environmentally friendly modes of transport, especially railway transport. For this reason, it is very important to ensure sufficient capacity of the railway infrastructure and high-quality railway transport operations. Railway transport control, operation, and management bring several specifications and unique features. One of the most important things is to correctly determine the capacity and throughput of the railway infrastructure because it must be clear how many trains can be operated on a concrete railway line for a certain time. Therefore, the issue of railway infrastructure capacity is a relatively broad and complex topic. Currently, there are several methods and ways to determine it. However, for scientific progress and research in this field, it is necessary to look for new scientific and professional solutions to the mentioned issue with effective implementation into practice. The mentioned contribution deals with new modern progressive methods of determining the capacity of the railway line using simulations and software applications. The main objective is to establish a methodology, specifically a heuristic procedure, in which specific partial steps of a new method of determining the capacity of railway infrastructure are defined. Subsequently, this new way of determining it is directly applied and explained on the specific railway line Bratislava–Komárno, which is located in southwestern Slovakia. The first part of the paper contains a theoretical framework and a brief explanation of the issue, including current used methods, as well as current scientific and professional manuscripts and papers that deal with this topic. Subsequently, the mentioned railway line is described, including the current operational problems arising on it due to insufficient current capacity. As part of the results, the proposal part is presented, including a universal heuristic procedure, which includes partial steps of the new methodology with application to the mentioned railway line. The discussions present its theoretical and practical benefits and topics for the further development of this issue. However, the most significant benefit will be the more effective identification of bottlenecks in railway operations, which will improve its smoothness and will have a significant impact on sustainable development and its aspects in the field of transport.