Given the importance of unit commitment risk (UCR) assessment in determining the probability of meeting load demand in the ahead short-term operation period, in this paper, a new analytical model for UCR assessment is presented. In the proposed model to consider the impact of wind power participation in the entire short-term period of operation of the system, using the developed risk area concept, a new model for UCR assessment is presented. Furthermore, uncertainties of wind power and load demand are considered simultaneously. Unlike the models presented in previous research for UCR assessment, which consider the share of wind power in the last period of operation, the proposed model for UCR assessment considers the share of wind power in all periods of operation. The proposed model was tested and evaluated on the RBTS system with a wind farm. Moreover, the results obtained from the simulation were reported. According to the results, in all cases, the value of UCR in the proposed model is lower than the modified PGM (M-PGM) method. The effectiveness of this innovative approach in evaluating the UCR of the power system despite wind power and load uncertainties was confirmed based on the results.