Abstract: Subway security inspection should be improved during some important periods when cities take over important events. In this paper social welfare effects of reinforced subway security inspection during the special period are analyzed, and then they are compared with those of the universal subway security inspection. In general, a passenger maybe a potential attacker or a normal passenger. Because of the limits of technology, the checking accuracy of X-ray checking machine for screening potential attackers is highly correlated with the false alarm rate for normal passengers. Thus, the optimal security inspection accuracy of checking machine needs to be analyzed. First, we summarizes the management characteristics of the universal and special subway security inspection processes are summarized. In the special security inspection, every of passengers must be accepted extra checking used the hand-held metal detector. Accordingly, the expected social welfare of the universal subway security inspection can be expressed as: SW^M=(1-t)·(V-P_F^M·(C_A+C_N))+t·(P_D^M·(d-C_A)-d), where t is the proportion of the potential attackers; P_D^F is the checking accuracy of X-ray checking machine for screening potential attackers; P_F^M is the false alarm rate of X-ray checking machine for screening universal passengers; V is the universal passengers' social welfare because of security inspection; C_N is the universal passengers' time cost because of extra artificial checking; C_A is the artificial checking cost; and d is the damage of terrorist attack. Similarly, the expected social welfare of the special subway security inspection can be expressed as: SW₁^M=(1-t)·[V-C_A-C_N-(C_A+C_N)·P_F^M1]+t·[(1-θ)(d-C_A)·P_D^M1-(1-θ)d-(1+θ)C_A], where θ is the proportion that potential attackers carry hazardous material with them, and the superscript 1 represents the special security inspection. Second, we discuss the different effects of the hand-held metal detector and the X-ray screening instrument on deterrence of potential attackers, convenience of universal passengers, and social welfare. In particularly, the accuracy of X-ray checking machine is measured as P(attacker alarm), where a higher value for this probability implies a greater deterrence for attackers. Similarly, the inconvenience effect for normal passengers is measured as P(inspect normal passenger), where a higher numerical value implies a greater inconvenience of normal passenger. Last, we make the numerical analysis about the impact of hand-held metal detector. Thus, we can get the following conclusions. Compared with the universal subway security inspection, the accuracy of X-ray checking machine can be reduced in the special case, in order to reduce the false alarm rate and inconvenience for normal passenger. Because the accuracy of X-ray checking machine in the universal subway security inspection is higher, it can effectively screen the potential attackers with the larger probability. However, only under some special conditions, the extra strengthening measures of subway security inspection, such as the hand-held metal detector, can improve total social welfare in the special subway security inspection. Thus, it is necessary to improve hardware devices according to some scenarios. The study provides some management measures for subway security.

Key words: optimized model, terrorist attack, subway security, special period, X-ray machine, social welfare