Health prognosis is an advanced process to forecast the future state of systems, structures and components. Even if it is now recognized as a key enabling step for the maintenance performance improvement on systems and structures, the issue of post-prognosis maintenance decision-making (i.e., how to use prognosis results to eventually make maintenance decisions) remains open. Faced with this situation, we propose a parametric predictive maintenance decision framework that can take into account properly the system remnant life in maintenance decisions. Unlike more classical frameworks, it uses the estimated precision on the prognosis of the system residual useful life as a condition index to decide for and to schedule the interventions on the system. The proposed framework is developed for a single-unit stochastically deteriorating system, maintained through inspection and replacement operations. Using results from the theory of semi-regenerative phenomena, the analytical maintenance cost model is derived for the long-run expected maintenance cost rate. The proposed maintenance decision structure is compared to a classical benchmark framework; numerical experiments evidence the performance and the robustness of the new framework, and confirm the benefit of basing maintenance decisions explicitly on the precision of the system health prognosis (and not only on e.g., the mean value of the estimated residual life).