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Fatigue crack damage depends on a number of stress range cycles. This is a time factor in the course of reliability for the entire designed service life. Three sizes are important for the characteristics of the propagation of fatigue cracks - initial size, detectable size and acceptable size. The theoretical model of fatigue crack progression can be based on a linear fracture mechanic. Depending on location of an initial crack, the crack may propagate in structural element e.g. from the edge or from the surface. When determining the required degree of reliability, it is possible to specify the time of the first inspection of the construction which will focus on the fatigue damage. Using a conditional probability and Bayesian approach, times for subsequent inspections can be determined. For probabilistic modelling of fatigue crack progression was used the original and new probabilistic method - the Direct Optimized Probabilistic Calculation (“DOProC”), which uses a purely numerical approach without any simulation techniques or approximation approach based on optimized numerical integration

Using DOProC method in reliability assessment of steel elements exposed to fatigue