The article is based on the analysis of the development of the theory of reliability and its indicators are formulated indicators of the reliability of transport systems and built a system of factors determining their reliability. It is established that the formation of the theory of reliability of transport systems today is not completed. Based on the specifics of the systems, new reliability indicators were proposed and substantiated such as emergency downtime and reliability of emergency downtime. On the basis of the performed studies, it was found that the specifics of the transport process require the introduction of emergency downtime close to the recovery time and the reliability of emergency downtime. It is necessary the introduction of two close parameters such as the average recovery time and the average emergency idle time. They are associated with the need to distinguish between the idle time of a technological system or a separate element when a failure occurs and the idle time is needed. For the technological links of the transport system, the main purpose of which is to ensure efficient operation transport process, the probability of emergency downtime can serve as a criterion for assessing their reliability.