AbstractThis paper provides a modelling framework for the use of non-homogeneous Markovian techniques for components and systems, where the sojourn time at a state, or a class of states, may be limited by a given value. This approach is useful, for example, to build component models with constant repair times, and to model systems or components with tolerable down times. Tolerable down time models have appeared in the field of Boolean techniques for 10 years. A systematic Markovian approach applied to systems composed of several components, allows the interdependencies among the components to be precisely treated, which may cause large conservativeness, if the Boolean modelling technique is applied.