Elevator system comprising at least one moving object (6, 21) configured for traveling along at least one guide member extending between a plurality of landings; a position sensor configured for determining the current position of the moving object (6, 21) along the guide member; at least one elevator safety device mounted to the moving object (6, 21) comprising: a safety controller; a memory; at least one engagement member (26a, 26b) movable between a non-actuated state in which it does not contact the guide member; and an engaged state in which it engages with the guide member; and at least one actuation member mechanically coupled with the at least one engagement member (26a, 26b) and movable between a non-actuated state; and an actuated state; characterized in that the at least one actuation member does not contact the guide member in the non-actuated state; the at least one actuation member contacts the guide member in the actuated state; and in that the safety controller is configured for: causing the at least one actuation member to move from the non-actuated state into the actuated state and storing within the memory a position of the moving object (6, 21) detected by the position sensor at a point of time within a given time frame around the moment in which the at least one actuation member is caused to move from the non-actuated state into the actuated state as a starting position; detecting the position of the moving object (6, 21) along the guide member after the actuation member has been moved from a non-actuated state into the actuated state; calculating the distance (d) between the detected position and the starting position; and determining that the elevator safety device has entered a fully activated state, in which the at least one engagement member (26a, 26b) engages with the guide member, when the calculated distance (d) between the detected position and the starting position reaches or exceeds a predefined limit. a safety controller; a memory; at least one engagement member (26a, 26b) movable between a non-actuated state in which it does not contact the guide member; and an engaged state in which it engages with the guide member; and a non-actuated state in which it does not contact the guide member; and an engaged state in which it engages with the guide member; and at least one actuation member mechanically coupled with the at least one engagement member (26a, 26b) and movable between a non-actuated state; and an actuated state; the at least one actuation member does not contact the guide member in the non-actuated state; the at least one actuation member contacts the guide member in the actuated state; causing the at least one actuation member to move from the non-actuated state into the actuated state and storing within the memory a position of the moving object (6, 21) detected by the position sensor at a point of time within a given time frame around the moment in which the at least one actuation member is caused to move from the non-actuated state into the actuated state as a starting position; detecting the position of the moving object (6, 21) along the guide member after the actuation member has been moved from a non-actuated state into the actuated state; calculating the distance (d) between the detected position and the starting position; and determining that the elevator safety device has entered a fully activated state, in which the at least one engagement member (26a, 26b) engages with the guide member, when the calculated distance (d) between the detected position and the starting position reaches or exceeds a predefined limit.