Nowadays, we are facing problems of global energy shortage as well as the need of environmental protection. The advantage of low cost and small amount of CO2 discharge makes nuclear power an important choice for energy. However, the safety of structures, systems and mechanical components employed in a nuclear power plant has to be assured before a plant can be constructed. One of the most important pressure boundary components in the steam supply system of a nuclear power plant is the reactor pressure vessel (RPV). It is welded together by several steel plates. Cracks occur more frequently in welds rather than in base plates of a RPV. When a predominant crack grows along with operating time to a certain size, it may result in brittle fracture in the weld of a RPV. It has been pointed out that clad thickness and crack size affect the embrittlement and fracture of the weld. The present study employs a probabilistic fracture mechanics approach by taking into account radiation embrittlement to find fracture-failure probabilities of RPV welds. The result shows that, when the clad is thicker than 0.35 inch, the failure probability at axial weld should be paid more attention to. As for the effect of inspection and repair, it is found that adopting a more advanced inspection instrument reduces failure probability more than increasing inspection cycles or covering more inspection areas. It is also found the probability of failure at circumferential welds is smaller than that at axial welds. The finding reassures the proposition made by the United States Nuclear Regulatory Commission (USNRC) that inspection of circumferential welds of a RPV can be exempted.