Hydrocarbons in the form of natural gas can be used in long-term energy production and could strengthen the defossilisation of the energy sector. However, operational reliability will decrease due to gas shortages in integrated energy systems. Correlations exist among the multiple failure patterns such as overloads of the transmission lines, overloads of the combined heat and power generator, and over-limit operations of gas compressors. The energy reliability assessment problem becomes more difficult to resolve for integrated energy systems than for power systems. This paper proposes an analytical method to address the multiple correlated risks that are caused by the energy network interactions in an integrated energy system. Three case results in MATLAB demonstrate the accuracy and computational efficiency of the proposed method. Compared to the Monte Carlo algorithm, which required approximately 550 s to obtain a precise failure probability with 50 thousand samples, the proposed method takes approximately 12.7 s to obtain an exact failure probability. The advantage is that, different from wide-bound theory and narrow-bound theory, the proposed method can offer a certain value rather than two bounds with respect to the failure probability. (C) 2019 Elsevier Ltd. All rights reserved.