## 6 Sensitivity Analysis
* Defective cost variation: The increase in the defect cost \(C_{def}\) (case vi) mainly caused major maintenance to be performed more frequently to renew the unit as quickly as possible and significantly reduce the quantity of defective items; this measure decreased the age \(A^{*}_{o}\). Additionally, it was observed that when increasing \(C_{def}\), the system reduced the inventory level since the presence of defects was more heavily penalized. This decision was complemented by decreasing the critical age \(A^{*}_{sub}\), which implied that the subcontractor must supply units at an earlier age to mitigate the presence of defects. The opposite effects were observed when the cost of defects decreased (case v). * Production cost variation: As the production cost \(C_{pro}\) increased (case viii), it was observed that major maintenance was performed at an earlier age as an attempt to ensure that the machine produced only flawless units; hence, the unit was functional for a shorter period, decreasing \(A^{*}_{o}\). Moreover, as \(C_{pro}\) increased, it was evident that the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Total**} \\ \cline{3-8}  & & \multicolumn{4}{c}{**Optimal Control Parameters**} & \multicolumn{2}{c}{**Cost**} \\ \cline{3-8}
**Cases** & **Par.** & \(Z^{*}\) & \(k^{*}\) & \(A^{*}_{o}\) & \(A^{*}_{sub}\) & \(TIC^{*}\) & **Effect** \\ \hline Base Case & - & 31.5 & 0.6707 & 150.32 & 100.8196 & 34.33 & Base of comparison \\ Case i & \(C^{+}\) & 39.83 & 0.692 & 154.84 & 107.1493 & 17.05 & \(Z^{*}\)\(\uparrow\), \(A_{o}\)\(\uparrow\), \(A_{sub}\)\(\uparrow\) \\ Case ii & & 14.93 & 0.627 & 140.36 & 88.0057 & 56.86 & \(Z^{*}\)\(\downarrow\), \(A_{o}\)\(\uparrow\), \(A_{sub}\)\(\downarrow\), \(A_{sub}\)\(\downarrow\) \\ Case iii & \(C^{-}\) & 16.58 & 0.6604 & 132.77 & 87.6813 & 66.10 & \(Z^{*}\)\(\downarrow\), \(A_{o}\)\(\uparrow\), \(A_{sub}\)\(\downarrow\) \\ Case iv & & 34.6 & 0.6718 & 154.47 & 103.7729 & 16.28 & \(Z^{*}\)\(\uparrow\), \(A_{o}\)\(\uparrow\), \(A_{sub}\)\(\uparrow\) \\ Case v & \(C_{def}\) & 32.21 & 0.6471 & 165.17 & 106.8815 & 23.42 & \(Z^{*}\)\(\uparrow\), \(A_{o}\)\(\uparrow\), \(A_{sub}\)\(\uparrow\) \\ Case vi & & 31 & 0.6875 & 139.85 & 96.1469 & 40.97 & \(Z^{*}\)\(\downarrow\), \(A_{o}\)\(\downarrow\), \(A_{sub}\)\(\downarrow\) \\ Case vii & & 32.19 & 0.6711 & 154.27 & 103.5306 & 14.10 & \(Z^{*}\)\(\uparrow\), \(A_{o}\)\(\uparrow\), \(A_{sub}\)\(\uparrow\) \\ Case viii & & 30.67 & 0.6705 & 145.46 & 97.5309 & 59.43 & \(Z^{*}\)\(\downarrow\), \(A_{o}\)\(\uparrow\), \(A_{sub}\)\(\downarrow\) \\ Case ix & \(C_{sub}\) & 30.66 & 0.6441 & 154.88 & 99.7582 & 24.68 & \(Z^{*}\)\(\downarrow\), \(A_{o}\)\(\uparrow\), \(A_{sub}\)\(\downarrow\) \\ Case x & & 33.61 & 0.7095 & 143.82 & 102.0403 & 47.66 & \(Z^{*}\)\(\uparrow\), \(A_{o}\)\(\uparrow\), \(A_{sub}\)\(\uparrow\) \\ Case xi & \(C_{R}\) & 31.53 & 0.6702 & 150.7 & 100.9991 & 27.96 & \(Z^{*}\)\(\uparrow\), \(A_{o}\)\(\uparrow\), \(A_{sub}\)\(\uparrow\) \\ Case xii & & 31.47 & 0.6715 & 149.87 & 100.6377 & 43.43 & \(Z^{*}\)\(\downarrow\), \(A_{sub}\)\(\downarrow\) \\ Case xiii & \(C_{M}\) & 30.78 & 0.6985 & 133.59 & 93.3126 & 25.46 & \(Z^{*}\)\(\downarrow\), \(A_{o}\)\(\uparrow\), \(A_{sub}\)\(\downarrow\) \\ Case xiv & & 31.93 & 0.6543 & 160.29 & 104.8777 & 40.26 & \(Z^{*}\)\(\uparrow\), \(A_{o}\)\(\uparrow\), \(A_{sub}\)\(\uparrow\) \\ \hline \hline \end{tabular} \(\uparrow\), and \(\downarrow\) shows the effect of the variation of the cost parameter.  
\end{table} 
Table 8: Sensitivities for the cost variations. inventory level \(Z^{*}\) decreased because internal production was more costly. Moreover, as the production cost increased, it led to reducing the critical age of utilizing the subcontractor \(A^{*}_{sub}\) because, in this context, it was more convenient for the company to have the subcontractor supply parts at an earlier age. As the production cost decreased, the opposite effects were observed (case vii).