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 one unified framework encompassing different kinds of lifetime distribution for failure coupling system. For typical complex networks, we found that three types of system lifetime distributions are emerged shaped by system size and failure coupling strength. When the failure coupling strength ϕ dominates, systems exhibit a cascade failure mode, the system lifetime following an exponential distribution as series systems due to long-range correlation. When the system size N dominates, systems exhibit wear-out failure mode, the system lifetime following the Gompertz model as parallel systems due to short-range correlation. When N and ϕ have comparable impact on systems, system lifetime follows a modified Weibull distribution. We find the critical failure coupling strength and critical system size which are helpful to identify the failure mode switch point. We provide rigorous theoretical analysis for emerged lifetime distribution. We reveal the microscopic mechanism of system lifetime distribution switch pattern by analyzing the competence between correlation length and network diameter. Finally, we verify our conclusions in real networks. Our study will help to understand the lifetime origin of complex systems and design highly reliable systems.