A multiple integral representation has been developed to analytically model the probability of failure of reactor vessel. The probability of fracture is a basic methodology for projecting for the life of a new vessel as well as to estimate the remaining life of an existing vessel. The integral representation for the probability of fracture calculation is based on the number count of critical cracks across the whole section of a vessel, based on a given calibrated crack distribution function, obtained by experimental examination of the vessel cross section. Multiple integral is implemented because of the degraded, or variable, fracture toughness and other factors representing the variable facture toughness. For example, the nuclear reactor vessel that is subjected to neutron radiation, will increase the reactor vessel steel brittleness. The effect of neutron irradiation can be calibrated by its increase in ductile-brittle transition temperature (DBTT) in fracture toughness versus temperature curve. Higher DBTT implies a decrease in fracture toughness and an increase in the chance of vessel fracture in brittle fracture mode. The extent of degradation that the High Flux Isotope Reactor (HFIR) vessel has experienced is characterized by its probability of fracture in this paper. The fracture probabilities under the accident pressure conditions against possible HFIR operating life are calculated for the safety analysis of the reactor vessel. Conventional numerical methods of fracture probability calculation such as that adopted by the NRC-sponsored PRAISE CODE and the FAVOR CODE developed in this Laboratory are based on Monte Carlo simulation. Heavy computations are required. The present method of Probability Integral has been used to verify numerical results of approximately 8–10 reports on HFIR remaining-life calculations by Cheverton using FAVOR CODE for the installation of HFIR new cold neutron source. The numerical result based on the method of Probability Integral confirms almost exactly as compared with that obtained by Monte Carlo Method adopted by FAVOR CODE. This Method of Probability Integral, because of its analytical structure, shows the clear physical interpretation of the fracture probability. It provides simple and expedient procedure to obtain numerical values of fracture probability. Moreover, it retains all possible features that the Monte Carlo Method of simulation can accomplish.

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