[en] A theoretical investigation is presented on the reliability assessment of nuclear reactor pressure vessels. In the analysis, a Poisson-type random walk model is assumed to represent the randomly occurred transients, which have randomly distributed stresses. These transient stresses cause a predominant initial crack size to grow and, therefore, degrade the reliability of a pressure vessel. Following the probabilistic fracture mechanics approach, the variability of the material properties is considered. A numerical calculation is carried out based on available empirical data. It is found that for a typical BWR pressure vessel, the failure probability lies in the order of 10^-6 and the failure rate is approximately in the order of 10^-8 per vessel year. The result is in agreement with other published results. (author)