Emergent lifetime distribution from complex network systems aging

TL;DR

This paper introduces a unified framework for understanding lifetime distributions in failure-coupled network systems, revealing how system size and failure coupling influence the emergent lifetime behavior.

Contribution

It develops a comprehensive model that captures different lifetime distributions and derives a fundamental thermodynamic equation for failure-coupled systems.

Findings

Lifetime distribution can be described by a modified Weibull model.

Distribution degenerates into Gompertz or exponential models depending on parameters.

Derived asymptotic lifetime distribution and fundamental thermodynamic equation.

Abstract

Most theoretical analysis for lifetime distribution explains origins of specific distribution based on independent failure. We develop a unified framework encompassing different lifetime distribution for failure-coupled network systems. We find three types of system lifetime distributions emerged from competence between system size N and failure coupling strength $\phi$. System lifetime distribution can be describe by modified Weibull model, which degenerates into Gompertz model when N dominates and exponential distribution when $\phi$ dominates. We derive asymptotic lifetime distribution. Specially, we derive a fundamental equation of thermodynamics for failure-coupled systems. Our study will help design highly reliable systems.