In recent years, the importance of resilient critical infrastructures has become more evident. More frequent extreme weather conditions and human-induced disasters, such as terror attacks, cause severe damage to infrastructures. It is important to be able to withstand such events, but perhaps even more important be able to bounce back and rapidly recover. In this work, resilience is formulated, in a pragmatic way, as a combination of the reliability of infrastructure elements, vulnerability and the recoverability of the failed components. To be able to characterize the recovery time, there is a need to know the reliability and vulnerability of the infrastructures, i.e. their drop in performance in different scenarios with different stress level. Moreover, recovery time and vulnerability can be affected significantly by different factors such as location, seasonal effects, recovery crew available etc. Hence, the trajectory of the loss in performance and the recovery may have different paths depending these associated factors, meaning that resilience prediction model must be able to capture these factors. However, resilience studies are not well detailed regarding the effect of time dependent and time independent influence factors. The proposed formulation makes it possible to predict the resilience of a (critical) infrastructure with multiple failure mechanisms, different types of vulnerability process, and recovery actions with time-dependent and time-independent covariates. © 2017 Taylor & Francis Group, London.