The object of research is the reliability indicators of the Pridnestrovian gas transmission system (Moldova). The conducted research is based on the mass service theory. This research is aimed at studying reliability indicators in terms of determining the quantitative composition of performers and the period of system failure elimination as the most cost-effective aspects of gas transmission organization activities. Since gas consumption facilities are growing annually, the further improvement of the reliability quality of the maintenance system is required. At the same time, as the service life of existing systems increases, the probability of its elements failure increases, which may result in reduced or complete loss of serviceability. It is the reliability indicator that reflects this process and represents a quality characteristic attributed to time. These questions can be solved by mass maintenance theory by investigating a random process and presenting it with a mathematical model of reliability. The proposed method of mass service system research reveals that incoming flows can be considered as Poisson’s (simplest) models, and in most cases it is possible to obtain satisfactory indicators of accuracy in solving the problem. As a result of the construction of a mathematical model, the analysis of existing failures in work by categories was carried out. Using the Kolmogorov criterion, it was determined that the experimental process for distributing applications is Poisson (the simplest). The average time to eliminate the system failure and the average value of the work performers were obtained, and it was also revealed that the irrational use of the calculated resources can lead to irreversible processes. Application of the proposed mathematical model for determination of reliability indicators will be effective also at operation not only of engineering systems but also of other objects of heat and power region due to the complex approach to realization of questions on accident-free activity of objects, both at design stage and at operation.