# A Modeling of Human Reliability Analysis on Dam Failure Caused by Extreme Weather
## 4 Bayesian Network Construction
### Bayesian Network Construction
However, since the effects of extreme weather on mindset and attention are not of the same cause or negligible, they cannot be deleted. By such screening, the stereotyped dependencies of the directed acyclic graph of a Bayesian network are derived. By consulting with experts and dam site managers, the conditional probabilities were populated using interpolation rules and assuming prior probabilities for the root node. Using binary nodes, where nodes have two possible states, \"success\" and \"failure\", the corresponding impact factor nodes are defined as \"positive\" and \"negative\". Positive states improve correlation performance, improve human reliability, and reduce the probability of human error, while negative states do the opposite. Ref. [45] suggests that the positive and negative states take values of 0.95 and 0.05, respectively, and the remaining non-root nodes are quantified using the interpolation principle in BN. The interpolation rule uses two parameters to populate the CPT, the probability that the child node is in a positive state when all parents are positive and when all parents are negative, which are taken as 0.90 and 0.10, respectively. The intermediate states are given by the following equations. \[\Pr(\max)=\text{MIN}+(\text{MAX}-\text{MIN})\times\frac{k}{N}, \tag{5}\]  
\[\Pr(\min)=1-\Pr(\max), \tag{6}\]  
where \(\Pr(\max)\) represents the probability that the child node is in a positive state and \(\Pr(\min)\) represents the probability that the child node is in a negative state. MAX denotes the probability that the child node is in a positive state when all parents are positive, and MIN denotes the probability when all parents are negative. k is the number of parent nodes with positive states, and N is the total number of parent nodes. Taking the Operator Quality Professional Skills node as an example, there are four parent nodes: Operator Physical IQ, Operator Quality Knowledge, Operator Quality Experience, Organization Atmosphere Training. So, it has 24 = 16 states, and the results obtained using the interpolation principle are shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Operator Physical IQ**} & \multirow{2}{*}{ \begin{tabular}{c} **Operator Quality** \\ **Knowledge** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **Operator Quality** \\ **Experience** \\ \end{tabular}  } & \multicolumn{2}{c}{ \begin{tabular}{c} **Organization** \\ **Atmosphere** \\ **Training** \\ \end{tabular}  } & \multirow{2}{*}{\(\mathbf{k}\)} & \multirow{2}{*}{**Positive**} & \multirow{2}{*}{**Negative**} \\ \hline Positive & Positive & Positive & Positive & 4 & 0.90 & 0.10 \\ Positive & Positive & Positive & Negative & 3 & 0.70 & 0.30 \\ Positive & Positive & Negative & Positive & 3 & 0.70 & 0.30 \\ Positive & Positive & Negative & Negative & 2 & 0.50 & 0.50 \\ Positive & Negative & Positive  
Using this approach, where the idea considered is that the negative state of each parent node will affect and have the same effect on the child nodes, since the impact of a change in the parent on the child nodes is not directly measurable in many cases, such an assumption of parity is used. Under this assumption, the more parents are in a negative state, the more human reliability decreases. The probability of each child node can be obtained by reasoning from Equation (3). If there is a child node \(a\) and its parent nodes are \(b\) and \(c\), the probability that it is in a positive state is:  
\[ \begin{array}{ll}P(a=a_{max})=&\mathrm{P}(a=a_{max}|b=b_{max},c=c_{max}) \times P(b=b_{max})\times P(c=c_{max})\\ &+\mathrm{P}(a=a_{med}|b=b_{max},c=c_{min})\times P(b=b_{max})\times P(c=c_{ min})\\ &+\mathrm{P}(a=a_{med}|b=b_{min},c=c_{max})\times P(b=b_{min})\times P(c=c_{ max})\\ &+\mathrm{P}(a=a_{min}|b=b_{min},c=c_{min})\times P(b=b_{min})\times P(c=c_{ min})\end{array}