The structural integrity of nuclear graphite, a crucial material within the reactor subjected to thermal, irradiation, mechanical, and other loads, is essential for the reactor's operation and must be evaluated for potential failure. To assess the failure probability of domestically produced graphite materials used in micro-gas cooled reactors, this study initially calculated and compared the failure probabilities of a large graphite brick. Subsequently, a compression test was conducted on a domestic graphite brick to validate its Weibull distribution. The failure probability was evaluated using KTA 3232 and the ASME 2015 and ASME 2023 distributions. The results indicated that the ASME 2015 assessment was overly conservative, while the ASME 2023 assessment demonstrated improvements compared to the 2015 version. For the evaluation of the failure probability of this domestically produced fine-grained nuclear graphite, it is necessary to propose a more reasonable model that simultaneously meets the requirements of prediction accuracy and conservatism, and can obtain a strength dispersion that is consistent with the experimental test results.