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

TL;DR

This paper presents a combinatorial algebra approach for complete enumeration of multicuts in k-out-of-n:F systems, aiding in reliability analysis and understanding structural differences.

Contribution

It introduces a novel algebraic method for enumerating multicuts in specific reliability systems, enabling comprehensive structural and computational analysis.

Findings

Complete multicut enumeration for k-out-of-n:F systems

Identification of structural differences between system types

Analysis of computational challenges in multicut enumeration

Abstract

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.