  Ceramic is a material frequently used in industry because of its favorable
properties. Common approaches in shape optimization for ceramic structures aim
to minimize the tensile stress acting on the component, as it is the main
driver for failure. In contrast to this, we follow a more natural approach by
minimizing the component's probability of failure under a given tensile load.
Since the fundamental work of Weibull, the probabilistic description of the
strength of ceramics is standard and has been widely applied. Here, for the
first time, the resulting failure probabilities are used as objective functions
in PDE constrained shape optimization.
  To minimize the probability of failure, we choose a gradient based method
combined with a first discretize then optimize approach. For discretization
finite elements are used. Using the Lagrangian formalism, the shape gradient
via the adjoint equation is calculated at low computational cost. The
implementation is verified by comparison of it with a finite difference method
applied to a minimal 2d example. Furthermore, we construct shape flows towards
an optimal / improved shape in the case of a simple beam and a bended joint.
