Joint Interval Reliability for Markov Systems with an Application in Transmission Line Reliability

NoWe consider Markov reliability models whose finite state space is partitioned into the set of up states View the MathML source and the set of down states View the MathML source. Given a collection of k disjoint time intervals I¿=[t¿,t¿+x¿], ¿=1,¿,k, the joint interval reliability is defined as the probability of the system being in View the MathML source for all time instances in I1union or logical sumcdots, three dots, centeredunion or logical sumIk. A closed form expression is derived here for the joint interval reliability for this class of models. The result is applied to power transmission lines in a two-state fluctuating environment. We use the Linux versions of the free packages Maxima and Scilab in our implementation for symbolic and numerical work, respectively