# Modelling a Safety Management System Using System Dynamics at the Bhopal Incident
## 3 System Dynamics Applied to the Bhopal Incident  
Starting from the causal loop diagram (CLD) developed above, a model in Powersim Studio was built. In order to validate the model proposed, all the data used for the simulation referred to the Bhopal incident, as they are available in the literature [20; 21; 22]. The probabilities of mechanical failure of the safety protection system have been expressed through appropriate aging functions, as in Figure 2. The following functions were introduced:  
1. Maintenance planning index, which considers the maintenance schedule on the plant. 2. Loss inspection likelihood, which takes into account human error in doing visual inspections that may be due to many variables (training, information, etc.) and certain conditions (stress, daytime, etc.) [16]. 3. System damage factor, which considers the impact of management on the production system. The interaction of all these variables, described above, led to the creation of the dangerous material leakage function. The main part of the model moved to the probability of loss of containment of hazardous material (Figure 3). The impending industry and safety 4.0 and the development of the related technologies, such as Internet of Things (IOT), Industrial Internet of Things (IIOT), digital twin, augmented reality and wireless communication technologies, will allow better data collection and in less time [9]. Figure 2: System dynamics diagram of mechanical system. The model proposed describes comprehensive plant safety systems (lock valves, cover jacket, depressurization valves), which are linked in Figure 3 with protection measures (refrigeration, washing systems, release valves, sprinklers). According to the values considered in [6], thanks to the development of the simulation methodology [21] in (Figure 4) an initial loss of about 300 min leading to an outlay of about $250,000 is shown. In the model, the function that links the labor force to the available capital has been obtained by interpolating available data in [20]. The Tables 1 and 2 show the human resources data in terms of educational level of operators and system safety. The relationship between the safety plant level and its workforce (WF) is shown in Figure 5. The capacity of carrying out all the ordinary tasks in time decreases while the workforce goes down. Figure 4: Economic loss function. Figure 3: System dynamics diagram—management loops. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Operators**} & \multicolumn{3}{c}{**Year**} & \multicolumn{3}{c}{**1979/1980 [1]**} & \multicolumn{3}{c}{**1981-1982 [3]**} & \multicolumn{3}{c}{**1984 [5]**} & \multicolumn{3}{c}{**November 1984 [7]**} \\ \cline{2-13}  & **Weight** & **\$/month** & **\$/year** & **\#** & **WF** & **\$/Year** & **\#** & **WF** & **\$/Year** & **\#** & **WF** & **\$/Year** & **\#** & **WF** & **\$/Year** & **\#** & **WF** & **\$/Year** \\ \hline operators BSC/diploma & 1 & 800 & 9600 & 2 & 2 & 19,200 & 8 & 8 & 76,800 & 2 & 2 & 16,000 & 2 & 2 & 1600 \\ Operators High School & 2 & 1000 & 12,000 & 15 & 30 & 180,000 & 0 & 0 & 6 & 12 & 60,000 & 6 & 12 & 6000 \\ Shift Supervisors & 3 & 1200 & 14,400 & 3 & 9 & 43,200 & 2 & 6 & 28,800 & 1 & 3 & 12,000 & 1 & 3 & 1200 \\ Maintenance Supervisors & 5 & 1600 & 19,200 & 3 & 15 & 57,600 & 2 & 10 & 38,400 & 1 & 5 & 16,000 & 0 & 0 & 0 \\ Plant Suptd & 6 & 1800 & 211,600 & 0 & 0 & 0 & 2 & 12 & 43,200 & 1 & 6 & 18,000 & 1 & 6 & 1800 \\ \hline \multicolumn{13}{c}{**Total Work Force**} & \multicolumn{3}{c}{56} & 30,000 & 36 & 187,200 & 28 & 122,000 & 23 & 10,600 \\ \hline Variatio than 1979–1980 & & & 0.00\% & & 35.71\% & & 50.00\% & & 58.93\% & \\ Variatio than 1981–1982 & & - & - & 0.00\% & & 22.22\% & & 36.11\% & \\ Variatio than 1984 & & - & - & - & 0.00\% & & 17.86\% & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Human resources data. In Figure 6, the value of the minimum workforce required under standard conditions, in order to prevent accidents in the plant, is also shown.