Civil engineering structures are commonly monitored to assess their structural behaviour, using alarm thresholds to indicate when contingency actions are needed to improve safety. However, there is a need for guidelines on how to establish thresholds that ensure sufficient safety. This paper therefore proposes a general computational algorithm for establishment of reliability-based alarm thresholds for civil engineering structures. The algorithm is based on Subset simulation with independent-component Markov chain Monte Carlo simulation and applicable with both analytical structural models and finite element models. The reliability-based alarm thresholds can straightforwardly be used in the monitoring plans that are developed in the design phase of a construction project, in particular for sequentially loaded structures such as staged construction of embankments. With the reliability-based alarm thresholds, contingency actions will only be implemented when they are needed to satisfy the target probability of failure.