## 2 Reliability Modeling of the Natural Gas Supply Chain
### Modeling of Key Influencing Factors in the Natural Gas Supply Chain  
The reasons for supply chain dysfunction include insufficient supplier capacity and demand uncertainty on the customer side [20]. The key factors affecting the natural gas supply chain are typically policy regulations and economic market fluctuations, which respectively affect the supply side and the demand side of the natural gas supply chain. The proactive promotion of low-carbon energy transformation policies will reduce the use of heavily polluting energy sources such as coal to a certain extent and increase the proportion of natural gas, leading to further increases in the natural gas supply and demand. However, changes in the international situation [21], such as the Ukrainian crisis, have greatly altered  
Figure 2: Equivalent diagram of a connection mode of minimal cut set. the natural gas trade pattern. The reduction in the natural gas supply by Russia has caused a tight supply situation, leading to a sharp increase in gas prices in Europe. Similarly, high gas prices have also suppressed the natural gas demand in Asia, leading Southeast Asia to choose other energy sources such as coal and nuclear power as substitutes. Similarly, many other factors such as significant supply and demand fluctuations caused by the COVID-19 pandemic have led to large fluctuations in fossil energy and electricity prices, which have to some extent affected the natural gas supply. To build an environmentally friendly power system, changes in government policies and regulations can limit the amount of corresponding energy supplied by suppliers, the same as the natural gas supply chain [22]. In addition, when the economic situation fluctuates and the price of natural gas increases, residents may seek alternative resources to replace natural gas, which is equivalent to reducing the supply of gas from the gas source in the natural gas pipeline system. When market policies are regulated and the economic environment is volatile, the gas supply from the source \(S\) can be multiplied by a factor \(\kappa\), expressed as \(S^{\prime}=\kappa\times S\). The compressor in a natural gas pipeline system serves a similar function to a step-up transformer in a power grid by raising the pressure level at transmission nodes in the gas network to compensate for pressure loss [23]. However, compressors consume 3% to 5% of the flow passing through them [24]. It is assumed that the natural gas flow is balanced at the compressor under normal conditions, with no loss or increase in flow. If a compressor fails during operation, the gas-transmission capacity of the pipeline connected to the station site is considered to decrease due to changes in the air pressure difference between upstream and downstream pipelines directly connected to it. The degree of decrease is determined by the degree of damage to the compressor set. The sub-station enables filtration, separation of gas impurities, and heating of the gas. If the sub-station is damaged, the quality of natural gas on the customer side will be reduced and the effective gas volume greatly reduced, leading to a decrease in the gas-transmission capacity of the pipeline [25; 26]. Therefore, if damage occurs in the pressure station, the pressure sub-transmission station, or the sub-transmission station, the gas-transmission capacity \(S\) will be decreased from \(\gamma_{c}\%\), \(\gamma_{cd}\%\) and \(\gamma_{d}\%\) to \(S^{\prime}\), denoted as \(S^{\prime}=(1-\gamma_{i}\%)\times S\). As for the pipelines in the gas system, when a rupture or leak occurs in the natural gas pipeline network, it is assumed that the pipeline will not be able to complete its transmission task, and the pipeline's capacity at that point can be expressed as \(S^{\prime}=0\). Therefore, the modeling of the impact of key factors on each link of the supply chain is shown in Figure 3[27], where \(\lambda\) is a 0-1 variable, with \(\lambda=1\) representing the failure of each link, and \(\lambda=0\) representing a normal operation of each link [28].