The behavior of structural systems can change during their service lives due to unexpected loadings, environmental effects, and deterioration processes. In order to optimize maintenance interventions, the life-cycle of a structure has to be properly assessed.Structural Health Monitoring (SHM) using collected experimental data provides a method for assessing the structural behavior over time. Since the cost related to SHM is substantial, sometime monitoring is limited in space and time.The modeling of the structural behavior based on few experimental data is characterized by uncertainty both in the choice of the appropriate model (epistemic uncertainty) and in parameters estimation (aleatory uncertainty).This paper provides an original procedure to support decisions in the presence of epistemic uncertainty. The procedure provides the development of a credibility index able to catch, between two possible models, which is the most reliable to describe the evaluation of parameters of interest.Considering as a case-study the occurrence of a foundation settlement in an arch bridge, the efficacy of the model proposed has been assessed. The approach can be applied to investigate the behavior of other aspects of the life-cycle assessment: the evolution of structural resistance, the failure time of an element or of the whole system.