An infrastructure system is inherently complex, with layers of both explicitly defined and hidden or subtle interfaces with other infrastructure systems and human users. High availability is desired, which implies stringent requirements on reliability and safety. Reliability analysis typically starts at component or sub-system level and aggregates through the system functional hierarchy. Because of the system complexity, incorporating occurrences of all possible interactions and scenarios is not always practical and failure data is often limited. Moreover, there are unobserved events among the sub-systems distributing either randomly or with temporal trend. To facilitate reliability analysis amid the complex environment and uncertain data, this paper proposes a general framework on modelling and aggregating reliability for complex systems with distinctive statistical approaches. The underlying principles are illustrated and suitability of the proposed techniques with respect to available data is discussed. This study contributes to the assurance of life-long productivity of infrastructure systems thorough monitoring mechanisms that rely on reliability information.