In structures containing brittle materials, residual and/or heterogenous stresses may prevent cracks to propagate up to failure. Consequently, for such structures, crack arrest has to be accounted for and a weakest link hypothesis may not be applicable. A probabilistic crack propagation model is derived to describe instantaneous or delayed arrest phenomena. A time-dependent regime is induced by slow crack growth experienced by ceramics and glasses. A general expression is obtained in which instantaneous up to infinite propagation times can be modelled in a unified way. The results are illustrated on a case study dealing with propagation of cracks in a thin walled tube submitted to a temperature gradient through its thickness. Different types of propagation/arrest regimes can be identified.