Emergent lifetime distribution from complex network systems aging

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.