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The failure propagation process has always been a research hotspot in the field of complex system reliability. Most of the research studies focus on the inference of network structure, ignoring one of the most critical parameters for network reliability, failure coupling strength. Here, we develop a generative model describing the failure process to infer the failure coupling strength. Using this model, we generate the node failure sequences under different coupling strength and analyze the spatial properties of failure propagation. We find the failed nodes tend to appear near the previously failed nodes with increasing coupling strength. Based on our generative model, we propose a Bayesian inference method to infer the failure coupling strength from observed system instantaneous failure state data. We find the inferred values are close to the true values for small failure coupling strength. As failure coupling strength increases, error comes from the limits of failure propagation spatial data. We apply this Bayesian inference method to actual biological networks and infer the network failure coupling strength. Our proposed Bayesian inference method helps analyze the hidden failure mechanism from actual scenarios. [ABSTRACT FROM AUTHOR]

• A model for failure coupling network is proposed. • Three typical lifetime distributions emerged from competence between system size and failure coupling strength. • Provide rigorous theoretical analysis for emerged lifetime distributions. • Microscopic mechanism of lifetime distribution is revealed by competence between correlation length and network diameter. 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. [ABSTRACT FROM AUTHOR]