The inherent brittleness of ceramics led to a probabilistic approach for designing with ceramic materials. For tackling this issue, numerous research projects led to the generation and continuous development of the weakest link postprocessor STAU over the last twenty years. Compared to other similar tools, STAU is unique in its comprehensive capabilities addressing spontaneous fracture, sub-critical crack propagation under transient loading, including a temperature-dependent fracture stress, and crack propagation parameters and analysis of strong stress gradients allowing for solving general thermo-mechanical problems including thermal shock and contact loading. Remarkably, the stress analysis, using commercial finite element codes, does not require a separate meshing with respect to the subsequent probabilistic analysis. Within the framework of a collaborative research effort (SFB 483) ceramics are qualified with respect to friction and wear for highly demanding applications. Here, uncertainty analysis methods for STAU were developed and led to an important extension of STAU for several technological applications. In this paper, the main features of STAU as well as the physical background are revisited and some application cases are shown.