Irreducible, continuous-time Markov models for reliability analysis are considered whose finite state space is partitioned as GℝB, where G and B stand for the set of system up (‘good’) and down (‘bad’) states, respectively. For a fixed length of time t0>0, let TG(t0) and NB(t0) stand, respectively, for the total time spent in G and the number of visits to B during [0,t0]. The dependability measure considered here is P(TG(t0)>t, NB(t0)•n), i.e., the probability that during [0,t0] the cumulative system up-time exceeds t(¸<t0) and the system does not suffer more than n failures. Using the ranodmization technique and some recent tools from the theory of sojourn times in finite Markov chains, a closed form expression is obtained for this dependability measure. The scope of the practical computational utility of this analytical result is explored via its Mat-Lab implementation for the Markov model of a system comprising two parallel units and a single repairman.
