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The paper provides an in-depth probabilistic integrity assessment of pressurevessels. Although the engineering integrity criteria have been fully observed, it has to betaken into consideration that the fracture properties, fracture quantities (the stress intensityfactor, J-integral) are random quantities or stochastic processes (time-dependentdegradation of fracture properties, crack size and crack growth). These principles form thebasis for equations from which a single defect failure risk is calculated, both for elastic andelastic-plastic state. The second part of the paper contains a calculation of the integralfailure risk for random number of possible structural defects.