To address effectively the urgent societal need for safe structures and infrastructure systems under limited resources, science-based management of assets is needed. The objective of this study is to develop an optimum life-cycle cost policy that suggests inspection/monitoring and maintenance actions based on the structural conditions in real time. Markov Decision Processes (MDPs) have a successful history of implementation in asset management of engineering structures. MDPs are controlled stochastic processes that advice the decision-makers to take optimum sequential decisions based on the actual results of the inspections or the nondestructive testings they perform. The focus in this paper is on Partially Observable Markov Decision Processes (POMDPs) where observations do not reveal the true state of the system with certainty. A specific example is presented, concerning corrosion of reinforcing bars in concrete structures, and a non-stationary POMDP, for an infinite horizon case, with 332 states is cast. Modeling and solving the decision-making framework is explained and the suggested method is compared with simpler techniques to verify its theoretical and practical supremacy.