As an integral feature of a future smart grid, demand response (DR) provides utility companies an emerging alternative to boost the reliability performance (e.g., supply adequacy) of power systems. Unlike for physical devices, the availability of DR is not only dependent on the operations of electric appliances on the demand side but can be affected by customers' behaviors. Thus, how or to what extent DR actions can affect power system reliability becomes an important issue for utilities. In this paper, a new approach for assessing the contribution of incentive-based DR to the supply adequacy of smart distribution systems (SDS) is presented. Compared with existing methods, our method explicitly captures the varying availability of customer DR capabilities. We introduce a behavior-reinforcement procedure to model the correlation of users' participation willingness with their historical DR profitability. Then, a strategic DR dispatch strategy can be developed to optimize users' DR availability bids in the market. In addition, the interdependency between a communication system and DR operation has also been considered. A hybrid algorithm based on sequential Monte-Carlo simulation and an optimal load dispatch method is employed to evaluate the system reliability in this context. The proposed approach is illustrated using both a small-scale test case and a real regional distribution grid in China. The results demonstrate the effectiveness of the presented method. (C) 2017 Elsevier Ltd. All rights reserved.