When the attacker attacks the time-critical targets, the timely turn-out probability is the most critical factor that influences the success rate. First, the timely turn-out operation is defined, and calculating formula for counting probability is derived. Secondly, the operation process of cooperative joint fire attack and attacker's operation process in integrative operation are analysed; the expected value and the maximum value of the turn-out time are gained. Finally, based on analysing the relationship between attacker's turn-out time and attack window, the timely turn-out probabilities under various conditions are calculated. The result of this research is useful in carrying out operations of attacking the critical targets.