It is essential to conduct a reliability analysis of systems with multiple types of components, and deal with the uncertainties within the components failure time distribution. Moreover, finding the most “critical” component in the system at a certain time facilitates a risk management. In this paper, we introduce the survival signature into a real world hydro power plant system and solve the epistemic uncertainties in the component’s failure time distribution. By implementing a relative importance index for each component, we can derive the reliability trend of the system depending on a component failure. The results show that the survival signature used on reliability analysis can help us deal with real world systems with more than one component type as well as to get bounds on system responses concerning epistemic uncertainties.