This paper introduces a novel mathematical approach to significantly enhance dual-axis solar trackers' Solar Reliability Factor (SRF) by developing and implementing an advanced Online Built-In Self-Test (OBIST) architecture. This innovative architecture is designed to efficiently address and correct single bit-flip errors within the system's microcontroller unit (MCU), a common control unit in contemporary solar trackers. By employing an improved diagnostic scheme based on extended Hamming codes, our OBIST architecture identifies and autonomously corrects all detected single bit-flip errors, reducing the fault coverage to 0%. This capability marks a significant advancement in the field, directly contributing to a substantial increase in the SRF by 47.48%. The study meticulously analyzes the potential fault domain influenced by environmental factors such as prolonged sunlight exposure and varying weather conditions, which are critical in the regular operation of solar trackers. Furthermore, we introduce a probabilistic model for defining and addressing stuck-at-faults, enhancing the system's overall reliability. The successful application of novel fault coverage-aware metrics demonstrates the OBIST architecture's effectiveness in improving solar tracker reliability, significantly contributing to the photovoltaic (PV) systems domain. This research presents a groundbreaking approach to enhancing solar tracker reliability and sets the stage for future advancements in the maintenance and efficiency of renewable energy systems.