Evaluating the integrity of a structure consists in proving its ability to realize its mechanical functions for all modes of loading, normal or accidental, and throughout its lifetime. In the context of nuclear safety, the most important structures consider the presence of a degradation grouping several aspects, such as cracks. In this context, the fracture mechanics provide the tools needed to analyze cracked components. Its purpose is to establish break criteria for judging loading margins in normal or accidental operating conditions. The seismic load is one of the dominant loads for the failure assessment of the pipes. Its probabilistic dispersion, however, was not taken into account in the past probabilistic fracture mechanics analysis. The objective of this paper is to simulate and analyze the effect of abnormal stress on the reliability of tow pipe sizes. As result the seismic stress has more effect on the break probability, but not for the leak probability. In the case without a seismic load, the break probability is mainly dominated by an initial crack size. The earthquake has much effect on the break probability for the large diameter pipe, not for the small diameter pipe. In the large diameter pipe, the break probability increases gradually with the time. The leak probability of both pipe sizes is not affected by the seismic curve.