Probabilistic security evaluation is one of the academic frontiers in the research on energy system reliability. It is very important to evaluate the impact of gas systems on the power/heat system for practical engineering in gas turbine engine-based integrated energy systems. This paper proposes a data-driven model instead of a physical model to estimate the probabilities of the incident of insufficient gas supply suffered from weather uncertainty, which affects the reliability of gas turbine engine-based integrated energy systems. According to actual energy projections, it can be assumed that the uncertainty of intermittent wind power, load fluctuations, and variations in gas deliverability derives from fluctuating weather conditions such as the temperature and wind. The wind power, load, and gas consumption data in the integrated energy system and the gas supply data of the station are sufficient to accurately build a data-driven model. Traditional methods based on physical models include the Iman and Stein methods, the first-order reliability method, and the mixed Monte Carlo algorithm to judge the effectiveness of the proposed method. The results from three cases are a testimony to the accuracy and engineering feasibility of the proposed method. The calculation of a data-driven model is easier than that of a physical model, and its simplification is conducive to failure probability estimation in a real application.