The paper has been intended to introduce a probabilistic method to estimate - from the standpoint of fatigue - the risk of a catastrophic failure to rotating (moving) members of an aircraft engine, i.e. to compressor blades. It has been assumed that there is a hidden defect in the material's structure, which initiates a small-size crack. Load-affected, the crack keeps growing. The crack propagation dynamics, when approached in a deterministic way, remains consistent with the Paris formula. The crack growth is effected by some random load characterised with the servicing load spectrum. While determining the load spectrum, all possible operational events are taken into account, excluding ones that could result in an immediate damage to the component. It has been assumed that random instances of load increase, which may result in an immediate damage, compose a separate set of events; hence, they have not been taken into account in this model. A partial differential equation of the Fokker-Planck type has been used to describe randomly approached dynamics of crack propagation. Having solved this equation enables a density function of the fatigue crack length to be found. This function, in turn, has been used to determine the risk of a catastrophic failure to a compressor blade. Furthermore, this function can also be used to find safe service life of the structure under consideration.