Abstract: A probabilistic method for determining an operability interval for fasteners in a nuclear power plant assembly includes providing a geometric distribution of a given initial condition of fasteners in the nuclear power plant assembly at an initial time T0; generating a plurality of random future fastener failure patterns by applying a fastener failure probability model to the geometric distribution at a given time T1>T0; inputting the plurality of random future fastener failure patterns at time T1 into a machine learning model and outputting stresses of the fasteners and displacements of the components; iterating, by a processor of a computer, the applying and inputting steps for a given range of time values T2, T3, . . .