The paper suggests a methodology to determine optimal reliability parameters (failure and restoration rates) of heat supply system components, which provide the required level of heat supply reliability. The methodological approach consists in the economically rational distribution of the total effect of reliability improvement among the system components, which is calculated using the average reliability parameters of the components. This task, along with the task to ensure structural reliability, is one of the key reliability tasks within a more general problem of optimal synthesis of heat supply systems and is urgent for both the systems under design and the existing insufficiently reliable systems. The methodology of solving the stated problem is based on the methods of the theory of hydraulic circuits, nodal reliability indices of heat supply, models of Markov random process and general regularities of cogeneration and heat transfer processes. The methodology also takes into account changes in thermal loads during the heating period and time redundancy of consumers related to heat storage. The results of the practical research based on the calculation experiment that confirms the viability of the presented methodology for the schemes of real heat supply systems are presented. The advantages of the proposed methodology compared to the existing approaches to solving this problem consist in joint optimization of the component reliability of heat source and heat network schemes, integration of procedures for the reduction in failure rates and the improvement in restoration rates of the components in one calculation pattern of search for the optimal system reliability, the absence of the need to conduct iterative calculations when using the average reliability parameters of components, considering the required levels of reliability indices.