U.S. Air Force Regulation 80-1 defines that a weapon system is composed of equipments, skills, and techniques, the composite of which ferns an instrument of combat. The complete weapon system includes all related facilities, equipments, materials, services, and personnels required for the operation of the system, so that the instrument of combat can be considered as a self-sufficient unit of striking power in its intended operational environment. Effectiveness of a weapon system can be expressed as a function of its liability, reliability and performance capability. Among these attributes which influence the weapon effectiveness, performance capability is considered to be the most critical factor for many weapon systems. In order to illustrate the application of the methodology of performance capability, a specific ease study on the effectiveness of Vulcan anti-air craft gun system is presented with special emphasis on hitting probability on moving targets, effects of artificial rounds dispersion, and several principles related to the deployment of the system. This thesis includes the thorough survey of the possibility of calculating the absolute value of hitting probability on moving targets, indicates that the effects of artificial rounds dispersion increase the value of probability only when the total number of rounds fired within fire range exceeds a certain critical number, and suggests that concentrated guns deployment is better than scattered deployment in order to obtain higher probability and lower average amount of rounds if it is assumed that the effects of counter-attack from enemy threats are not serious.