Joint interval reliability for Markov systems with an application in transmission line reliability

We consider Markov reliability models whose finite state space is partitioned into the set of up states image and the set of down states image. Given a collection of k disjoint time intervals image, image, the joint interval reliability is defined as the probability of the system being in image for all time instances in image. 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.