# The Development of a Cold-Chain-Packaging Risk Management Model Based on Fuzzy Bayesian Network
## 4 Case Study
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Risk Factor** & **What Can Cause It?** & \begin{tabular}{c} **What Are the Possible** \\ **Consequences?** \\ \end{tabular} \\ \hline Product safety risk & \begin{tabular}{c} Contamination, loss of vaccine \\ potency, over-thawing, \\ mechanical damage \\ Working in extreme cold \\ temperatures, improper \\ training on handling shipping \\ containers \\ \end{tabular} & \begin{tabular}{c} Vaccine not being effective, \\ health harm \\ \end{tabular} \\ Occupational safety risk & \begin{tabular}{c} Contamination, loss of vaccine \\ potency, over-thawing, \\ mechanical damage \\ Working in extreme cold \\ temperatures, improper \\ training on handling shipping \\ containers \\ \end{tabular} & \begin{tabular}{c} Injuries, cold-related diseases, \\ slips on cold surfaces \\ Temperature disruptions, \\ quality decay, safety hazards \\ Safety hazards, damage to \\ products, injuries, waste \\ Over-thawing, lack of \\ traceability, temperature \\ disruptions \\ \end{tabular} \\ Container risk & \begin{tabular}{c} Poor packaging used, poor \\ monitoring during cold chains \\ Insufficient training, vague \\ instructions, lack of sanitation \\ Insufficient monitoring \\ \end{tabular} & \begin{tabular}{c} Temperature disruptions, \\ quality decay, safety hazards \\ Safety hazards, damage to \\ products, injuries, waste \\ Over-thawing, lack of \\ traceability, temperature \\ disruptions \\ \end{tabular} \\ Conitoring risk & \
\begin{tabular}{c} Improper materials used, \\ improper capacity, unsafe \\ packages, packaging lacking \\ sustainability \\ \end{tabular} &
\begin{tabular}{c} Environmental hazards, \\ insufficient temperature \\ control \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Identified safety risk factors in cold chain packaging. Figure 4: BN model of safety risk of vaccine cold chain shipping containers. Figure 5 details the BN-based risk management model for vaccine cold chain shipping containers, and a sensitivity analysis was carried out. The purpose of a sensitivity analysis is to analyze the impact of changing an independent variable on a particular dependent variable, therefore showing how uncertainties in different inputs can affect the overall uncertainty of the model (13). To conduct sensitivity analysis, changes to the prior probabilities of one variable are needed, and the changes to the posterior probabilities are logged to assess the impact. For this case study, the variable 'packaging risk' is selected for sensitivity analysis, and seven different values are inputted, which include (0.19, 0.2, 0.21), (0.24, 0.25, 0.26), (0.29, 0.3, 0.31), (0.34, 0.35, 0.36), (0.39, 0.4, 0.41), (0.44, 0.45, 0.46) and (0.49, 0.5, 0.51). The corresponding posterior probabilities are calculated and shown in Table 9, and as P(P = P1) gradually increases, P(PS = PS1 | P = P1) steadily increases, which is also shown in Figure 6, validating the reliability of the results. \begin{table}
\begin{tabular}{c c c c} \hline  & & **P (C1 | P, M)** & **P (C2 | P, M)** \\ \hline \multirow{2}{*}{M1} & P1 & (0.74, 0.75, 0.76) & (0.24, 0.25, 0.26) \\ \cline{2-4}  & P2 & (0.34, 0.35, 0.36) & (0.64, 0.65, 0.66) \\ \hline \multirow{2}{*}{M2} & P1 & (0.54, 0.55, 0.56) & (0.44, 0.45, 0.46) \\ \cline{2-4}  & P2 & (0.04, 0.05, 0.06) & (0.94, 0.95, 0.96) \\ \hline \end{tabular}
\end{table} 
Table 6: The conditional probability of ‘container risk’ (C). \begin{table}
\begin{tabular}{c c c c} \hline  & & **P (PS1 | C, H)** & **P (PS2 | C, H)** \\ \hline \multirow{2}{*}{C1} & H1 & (0.84. 0.85, 0.86) & (0.14, 0.15, 0.16) \\ \cline{2-4}  & H2 & (0.34, 0.35, 0.36) & (0.64, 0.65, 0.66) \\ \hline \multirow{2}{*}{C2} & H1 & (0.59, 0.6, 0.61) & (0.39, 0.4, 0.41) \\ \cline{2-4}  & H2 & (0.01, 0.02, 0.03) & (0.97, 0.98, 0.99) \\ \hline \end{tabular}
\end{table} 
Table 7: The conditional probabilities of ‘product safety risk’ (PS).