This study presents an interval based robust chance constrained (IBRCC) optimisation model for allocating demand response program to effective buses of the power systems considering wind uncertainty and equipment failures. In the proposed formulation, an interval based robust approach is applied to evaluate the highest uncertainty spectrum of the wind power generation that the power system can tolerate. Accordingly, to cope with the uncertainty sources, chance-based constraints are implemented. In the proposed IBRCC optimisation framework, the level of the optimal solution robustness is probabilistically maximised subject to a set of operational constraints. Besides, to facilitate the massive integration of uncertain wind generation and to mitigate congestion in the transmission grid, an efficient allocation, and scheduling scheme of demand response programs is proposed. The proposed model is evaluated on the IEEE 24 bus system.