This paper addresses dynamic positioning of surface vessels moored to the seabed via a spread mooring system, referred to as position mooring. In normal weather conditions, the mooring system constrains the vessel and the controller applies thruster force for motion damping and heading control, only. In harsh weather, however, the mooring system becomes inadequate and thruster force is also needed for positioning in order to avoid damage to the mooring lines. While traditional position mooring systems apply thruster force based on constraining the vessel to lie within a predefined geographical region, the controller presented in this paper instead employs structural reliability measures to restrict movement. These structural reliability measures become an intrinsic part of the controller, automatically adjusting the allowed geographical region based on current weather conditions and structural properties of the mooring lines.