This article describes the issues related to the analysis of the reliability-exploitation of power supply systems in transport telematics devices (PSSs in TTDs). This paper characterizes solutions, which are applied in supply systems, and describes a PSS in a TTD from a main source and a standby one. This enables determining the dependencies denoting the probabilities of the system staying in full ability state, safety threat state, and safety unreliability state. A quality analysis of the PSS in TTD was conducted, and the indicator value of the supply continuity quality was evaluated. This indicator allows the demonstration of continuity quality of power supply (CQoPS) dependency on many quality dimensions, not just reliability. An example demonstrates the calculation of CQoPS factor for both the main and the standby power supply, employing three observations, each influencing the quality. The presented considerations in the field of quality and reliability-exploitation modeling of a PSS can be applied as well in other public utility facilities (including those classified as critical infrastructure). The character of functions performed by critical infrastructure facilities demands an operating continuity of these systems at an appropriate level. The co-first authors of the article once again address the issue of determining CQoPS factor, this time on the basis of modeling using mathematical evidence. TTD is an example in this article, because the presented methods can be used in any kind of system, especially in the power source of critical systems.