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. When environmental loads due to wind, waves, and current increase, thruster assistance is required also 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 designed in this paper instead employs structural reliability measures for the mooring lines to restrict movement. These structural reliability measures become an intrinsic part of the controller, enabling it to automatically adjust the admissible region for the vessel in the presence of changing winds, currents, and waves.