A Fast and Accurate Failure Frequency Approximation for $k$-Terminal Reliability Systems

TL;DR

This paper introduces a polynomial-time algorithm to approximate the failure frequency of large-scale $k$-terminal reliability systems with controllable error, significantly improving speed and accuracy over Monte Carlo methods.

Contribution

The paper presents the first polynomial-time approximation algorithms for failure frequency in $k$-terminal systems, including special cases with all-terminal reliability, with provable error bounds.

Findings

The algorithms run in polynomial time relative to the number of minimal cutsets or nodes.

The methods achieve higher accuracy and faster computation than Monte Carlo simulations.

Simulation results validate the efficiency and precision of the proposed approximation techniques.

Abstract

This paper considers the problem of approximating the failure frequency of large-scale composite $k$-terminal reliability systems. In such systems, the nodes ($k$ of which are terminals) are connected through components which are subject to random failure and repair processes. At any time, a system failure occurs if the surviving system fails to connect all the k terminals together. We assume that each component's up-times and down-times follow statistically independent stationary random processes, and these processes are statistically independent across the components. In this setting, the exact computation of failure frequency is known to be computationally intractable (NP-hard). In this work, we present an algorithm to approximate the failure frequency for any given multiplicative error factor that runs in polynomial time in the number of (minimal) cutsets. Moreover, for the special case of all-terminal reliability systems, i.e., where all nodes are terminals, we propose an algorithm for approximating the failure frequency within an arbitrary multiplicative error that runs in polynomial time in the number of nodes (which can be much smaller than the number of cutsets). In addition, our simulation results confirm that the proposed method is much faster and more accurate than the Monte Carlo simulation technique for approximating the failure frequency.