Consecutive-2-of-n:F systems with node and link failures

It has always been assumed that nodes can fail but not links, although most examples given for the consecutive-k-out-of-n :F system show no reason for such an assumption. The system described not only allows links to fail, but allows both nodes and links to fail, with distinct probabilities. For the k=2 case, the authors set up recursive equations for system reliability, and give a closed-form solution. It is proved that for n large, the reliability is decreasing in n (with one exceptional case) and higher reliability should be provided to the nodes, and then to the longer links rather than to shorter links