Usual strength and fatigue experiments for ceramic materials determine the failure behaviour at simple stress states with small stress gradients. Recently, ceramics have been also used in applications like gears and pumps because of their outstanding tribological properties compared to metals. The resulting contact loading causes a multi-axial inhomogeneous stress state with high stress gradients, which have to be considered in the experimental characterisation and failure prediction. A new method for prediction of the contact strength and contact fatigue behaviour of ceramic components under normal, sliding, and cyclic contact loading has been developed [1]. The method is implemented in a fast Contact Design-Tool (CDT), that works independent from FEM methods and can be used to assess the lifetime and the failure probability of the loaded ceramic. Results obtained from the Contact Design-Tool for the friction contact of a continuous variable transmission gear [2] show an exponential dependency of the maximum allowed normal pressure in dependency of the friction coefficient of the system. The results indicate, that contact fatigue under spherical loading of alumina is expected only for radii lower than 15 mm.Keywords: alumina, unlubricated sliding contact, friction, failure probability, fatigue