## 2 Methodology
### System Dynamics  
While the BN model incorporates HOEs, it does not consider their risk variation over time; the BN helps in the computation of risk value at a given time. Since the condition of building and equipment varies over its lifetime, it is natural to ask whether risk can be computed that varies \begin{table}
\begin{tabular}{c c} \hline \hline
**Basic Events** & **Probability (10\({}^{6}\) h)** \\ \hline Poor safety supervision & \(4.60\times 10^{-4}\) \\ Deficient training & \(1.89\times 10^{-3}\) \\ Not following procedures & \(1.70\times 10^{-4}\) \\ Deficient risk assessment & \(1.80\times 10^{-4}\) \\ Deficient knowledge & \(1.89\times 10^{-3}\) \\ Inexperience & \(1.10\times 10^{-3}\) \\ Insufficient technical handover & \(6.30\times 10^{-3}\) \\ Insufficient safety check & \(2.50\times 10^{-2}\) \\ Inadequate periodic inspection & \(2.50\times 10^{-2}\) \\ Invalid daily record & \(5.60\times 10^{-3}\) \\ Inadequate emergency plan & \(5.00\times 10^{-4}\) \\ Failure to read monitoring data correctly & \(2.50\times 10^{-3}\) \\ Design error of operator & \(2.20\times 10^{-3}\) \\ Failure to follow technical requirements & \(1.92\times 10^{-4}\) \\ Not following technical requirements & \(1.92\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Probability of relevant HOE basic events obtained from the literature [34; 35; 36; 37; 38; 39]. with time. Fire events are complex dynamic processes, yet HOEs can be analyzed utilizing SD modelling [41; 42]. This requires interaction of the BN with the SD model for the HOE variables. The SD model incorporated for this analysis extends the model in [17] to encompass HOEs based on the reliability associated with maintenance practices and perceived safety. From a more general view, the maintenance regime is a subsystem linked with other subsystems, such as building management strategy and organizational safety culture. The SD model is a two-step approach, the first being the causal loop diagram. A causal loop diagram is used to visualize the causal relationships in a system. It consists of all the elements representing the system and their interactions with each other including feedback loops and time delays, which are an integral part of the system. It helps conduct a qualitative analysis of the system's structure and behavior. The second step is the stock and flow diagram which is a quantitative analysis technique with the use of stocks and flows. Stocks are accumulations in the system and stocks are used to represent variables that change with time. Flows are entities that control these stocks. Flow entering a stock (_Entry flow_) increases the value of a stock and a flow exiting a stock (_Exit flow_) decreases its value. Mathematically, the relationship between stocks and flows is shown in (7):  
\[Stock=\int_{0}^{t}(Entry\_flow-Exit\_flow)dt \tag{6}\]  
In this approach, each node of BN is made equivalent to a node in SD model. For example, if one of the nodes of the BN is represented by state yes or no, it is assigned with a probability and represented as a single state variable in the SD model. To bring time-varying values into this variable, it is perturbed by a known value. For example, a variable _fireyes_ is associated with a normal probability value of 0.03. From experience, it is known that there is a variation of 25% on the probability values. This can be implemented as:  
\[P(fire:yes)=0.03\pm(25\%\;of\;0.03) \tag{7}\]  
For the child nodes, the conditional probabilities are calculated using the chain rule application of Bayes' theorem. The CPT shown in Table 2 is translated into an equation using the Boolean logic. Consider a child node 'inefficient timely control', which has three parent nodes--'deficient training', 'inefficient emergency plan', and 'not comply with instruction'. In the SD model, it is represented by the variables--'inefficient timely control yes' and 'inefficient timely control no' and can be translated into the following equations:  
\[