The operation of a system, such as a vehicle, communication network or automatic process, heavily depends on the correct operation of its components. A Stochastic Binary System (SBS) mathematically models the behavior of on-off systems, where the components are subject to probabilistic failures....

We analysed in the companion paper (Stochastic Process. Appl. 38, 1991), the conditions under which the aggregated process constructed from an irreducible and homogeneous discrete time Markov chain over a given partition of its state space is another homogeneous Markov chain. The obtained result...

We consider an irreducible and homogeneous Markov chain (discrete time) with finite state space. Given a partition of the state space, it is of interest to know if the aggregated process constructed from the first one with respect to the partition is also Markov homogeneous. We give a...