Efficient multicut enumeration of k-out-of-n:F and consecutive k-out-of-n:F systems

We study multiple simultaneous cut events for k-out-of-n:F and linear consecutive k-out-of-n:F systems in which each component has a constant failure probability. We list the multicuts of these systems and describe the structural differences between them. Our approach, based on combinatorial commutative algebra, allows complete enumeration of the sets of multicuts for both kinds of systems. We also analyze the computational issues of multicut enumeration and reliability computations.