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Current transport infrastructure in Europe depends on numerous steel and concrete-steel bridges, often from high-strength steel. One of the main engineering challenges related to such bridges is to ensure their reliability during their whole lifespan. It is not easy as load by automotive or rail transport typically induces fatigue effects, especially on steel parts. It is usually necessary to execute periodic inspections which should make possible timely detection of issues (cracks) which would make effective repairs possible. Thus, it is important to be able to plan these inspections in right times and to inspect the critical details with focusing on their fatigue damage. The paper discusses some challenges related to this approach. The Direct Optimized Probabilistic Computation method (DOProC) is combined with linear fracture mechanics analytical solution to find the time of the first inspection. Then it is assumed that modified solution can be used to find times of further inspections. In the paper there are discussed issues related to the speed of the DOProC in such application and the approaches to limit the computational time without a loss of precision. [ABSTRACT FROM AUTHOR]