## 3 Calculation Method of Risk Factor Coupling Coefficient  
### Basic Assumptions of Risk Factor Coupling Coefficient  
The coupling effect of risk factors is studied by using conditional probability. Firstly, the coupling coefficient of risk factors is defined and meets some basic assumptions. The minimum causal unit is assumed, as shown in Figure 1. Event C is the result, event \(\Gamma_{1}\) (c) and \(\Gamma_{2}\) (c) is the factor causing event C, abbreviated as \(\Gamma_{1}\) and \(\Gamma_{2}\). Figure 1a shows the case with only one factor and Figure 1b shows the case with two factors. It is assumed that the system in Figure 1a is \(S_{C}^{\mbox{\small\raisebox{-0.86 pt}{\small 1}}}\) and Figure 1b is \(S_{C}^{\mbox{\small\raisebox{-0.86 pt}{\small 2}}}\). On this basis, the following assumptions are made, as shown in Table 1.  
**Assumption 1**. : _When the risk factors (\(\Gamma\)) do not exist, the system risk is 0._  
During risk analysis, according to the amount of information available, an event \(C\) may be in three states of \"occurred\", \"not occurred\" and \"uncertain\", which are respectively expressed as:  
\[\left\{ \begin{array}{rl}P(C)=0,&C:Not\ occurred\\ 0<P(C)<1&C:uncertain\\ P(C)=1,&C: occurred\end{array} \right. \tag{1}\]  
When discussing a set of \(n\) events, there may be \(3^{n}\) possible state combinations for the events in this set, which is called a \"situation\". \"No risk factors occur\" refers to a situation in which all the causes obtained through causal analysis are in the state of non-occurrence. Which is expressed as:  
\[\left\{\begin{array}{rl}&S_{C}^{\mbox{\tiny\mbox{\tiny\mbox{\tiny\mbox{ \tiny\mbox{\tiny\mbox{\tiny\mbox{  
than the latter. Due to the relativity of risk factors, this nature should be established in all parts of the system. It can be inferred that when the risk factor occurs, the probability of all subsequent events is greater than when it does not occur. Under the condition of satisfying basic Assumption 1, basic Assumption 2 is naturally established in \(S^{\textcircled{1}}_{\text{C}}\) and can be expressed as the following formula in \(S^{\textcircled{2}}_{\text{C}}\).  
\[P(C)^{\textcircled{2}}_{\Gamma_{1}\Gamma_{2}}=P(C|\Gamma_{1}\Gamma_{2})\geq max \big{\{}P\big{(}C|\overline{\Gamma_{1}}\Gamma_{2}\big{)},P\big{(}C|\Gamma_{1} \ \overline{\Gamma_{2}}\big{)}\big{\}} \tag{4}\]  
**Assumption 3**. : _Under the same objective situation, the risk of the system remains unchanged and has nothing to do with the result of causal analysis._  
Basic Assumption 3 is closely related to the objective existence of risk factors. For the same result event \(C\), the causes of different causal analysis may be different, but these different analysis results objectively correspond to the same event. For example, \(S^{\textcircled{1}}_{\text{C}}\) and \(S^{\textcircled{2}}_{\text{C}}\)  
where the angle mark \"\(\Omega\)\" represents that the system is in any condition. Substituting Equations (3) and (6) into Equation (9), we can get:  
\[P\big{(}C\big{|}\overline{\Gamma_{1}}\,\Gamma_{2}\big{)}P\big{(}\overline{\Gamma _{1}}\big{)}P(\Gamma_{2})=0 \tag{10}\]  
This result is undoubtedly unreasonable. Through the analysis, it can be found that the reason for this result is the simplification of the basic probability in basic Assumption 1, which is not in line with the objective situation. This term in Equation (10) is rounded off by basic Assumption 1 as part of the basic probability in \(S_{C}^{\bigodot}\), but in \(S_{C}^{\bigodot}\), this part of the probability is explicitly expressed because \(S_{C}^{\bigodot}\) changes from implicit cause to explicit cause, resulting in this unreasonable result.