The gearboxes (reducing gears) built in the rotating excavators used at surface coal mines, are exposed to dynamic loads which are frequently unpredictable (stochastic) given the exploitation conditions. These gearboxes are very frequently oversized by the manufacturer. Nevertheless, the possibility of impact loads due to unpredictable working resistances the excavators run up against, can reduce the safety of the gearbox, even to the extent of breakdown of some of the constituent elements in given period till the planned overhaul. This paper presents the methodology for assessing the safety (reliability) of most unreliable gear in specific gearbox, being ascertained by the maintenance experience of the gearbox. Concerning this gearbox, the load function has been established based on experimental investigations, being presented in this paper. Regarding the most unreliable gear, the carrying capacity function has been established by means of theoretical research being displayed in the comparative diagram together with the load function. This comparative diagram helps to infer the safety of the most unreliable gear in the gearbox, i.e. the safety of the gearbox as a whole. The loading on the gearbox is a variable course of the rotating moment with the driven shaft depending on the time span during the total exploitation life of the gearbox. The carrying capacity of the gearbox is equal to the permissible temporally constant rotating moment acting on the driven shaft within a time span encompassing a number of changes in the loading on the driving shaft. The presented methodology can be applied to investigate the safety of other similar gearboxes.