Demand response (DR) has been considered as an effective method to provide regulation services for power systems. In order to achieve the precise control of flexible loads and fulfill the operator or aggregator requirement, the regulation capacity evaluation of DR becomes a significant problem. More seriously, equipment faults can make the capacity evaluation more difficult, such as the load faults, communication network faults, and terminal controller faults. Faced with this issue, this paper proposes an electricity price-demand elasticity (EPDE) matrix combined with the equipment faults rate to evaluate the regulation capacity of DR quantitatively. First, the concepts of EPDE, self-elasticity and cross-elasticity are proposed and formulated. On this basis, the equipment fault rate is formulated and combined with the EPDE matrix. Finally, the proposed models and methods are verified in case studies.