In this paper, an uncertainty assessment analysis extension is proposed for the inoperability input-output model (IIM), which is a methodology for assessing the propagated consequences of initial disruptions to a set of sectors. The IIM has been developed to help understand infrastructure interdependencies on deliberate external attacks or unfortunate natural disasters. Since the final demand perturbation may be affected by the psychological impact on consumers. In this paper, the uncertainty demand-driven IIM is extended to allow final demand perturbations in the form of lognormal probability distributions. The Monte Carlo simulation is used to demonstrate the uncertainty analysis methodology in detail through a four-sector economy system, and the results show that the value of interdependency analysis in the risk assessment process as an integral part of interdependent infrastructure.