Fluorocarbon gas c-C_4F_8 is one of the potential substitution candidates for SF_6 because of its low global warming potential (GWP) and high dielectric performance. Gas insulated switchgears using c-C_4F_8 gas mixture will be a new type of environment-friendly device. The decomposition gas analysis method is an important way for fault diagnosis by measuring the decomposition gases generated by electrical fault, which has an irreplaceable role in some situation. However, different criteria are needed for different insulation gases. In this paper, the gas decomposition properties of fluorocarbon were studied by the simulating experiments of four kinds of faults. Accordingly, a fault diagnostic criterion was proposed. The experiment results show the main decomposition gases are C_2F_4, C_3F_6 under overheating fault, and the ratio of C_2F_4/C_3F_6 is different in different overheating temperature zones. Different form the overheating fault, the main decomposition gases under discharges are CF_4, C_2F_6, C_2F_4, C_3F_8 and C_3F_6. Meanwhile, the ratios of C_2F_4/CF_4, C_2F_4/C_2F_6 and C_3F_6/C_3F_8 are quite different for partial discharge, spark discharge and arc discharge. Therefore, a dynamic three-ratio method was proposed to identify three types of discharge faults by ratio variation tendency, which provides a way for monitoring faults of c-C_4F_8 insulation equipment.