# JIT Production Strategy and Maintenance for Quality Deteriorating Systems
## 6 Sensitivity and Results Analysis  
The primary objective of this section is to proceed with further analysis of a set of experiments and analyze the sensitivity of several cost parameters. The aim of the analysis is to study the behavior of the proposed integrated model, and compare the value of the control parameters and the total incurred cost for different system conditions derived from a basic case. Table 6 presents ten different configurations derived from the variation of five cost categories. Figure 3: Cost projection of the estimated expected total cost. \begin{table}
\begin{tabular}{c c c c c c} \hline  & \(Z_{0}^{*}\) & \(k^{*}\) & \(A_{0}^{*}\) & **Total Cost Estimate** &
\begin{tabular}{c} **Cross-Check** \\ **Confidence Interval (95\%)** \\ \end{tabular} \\ \hline Factor & 132.02 & 0.3136 & 147.084 & 88.13 & [85.69, 91.22] \\ \hline \end{tabular}
\end{table} 
Table 5: Optimal control parameters and cross-check validation. The obtained results of the sensitivity analysis are presented in Table 7, and can be interpreted as follows:  
* Variation of the inventory cost: When the inventory cost \(C^{+}\) increases (case II), the proposed policy reacts by decreasing the production threshold \(Z_{p}^{*}\), since the inventory of products is more penalized. With the increase of such penalization, we also notice that product inventory is limited to the bare minimum, and so the system extends the JIT policy for a longer period of time, thus increasing age \(B_{JIT}^{*}\). By examining the results, we observe that the increment of \(C^{+}\) promotes the conduction of more frequent major maintenance as a countermeasure to ensure the production of flawless units. Thus, at increasing \(C^{+}\), the critical age for major maintenance \(A_{0}\)* reduces. When the inventory cost decreases, we note the opposite effects (case I). * Variation of the backlog cost: When the backlog cost increases (case IV), the shortages of products are more penalized, and thus the production threshold \(Z_{p}^{*}\) increases as a protection against the lack of product. Additionally, we note that product deficiency is also tackled by reducing the critical age \(B_{JIT}^{*}\), and with this measure the unit applies less time the JIT policy, thus keeping product inventory for a longer period of time. Upon further investigation, the increment of the backlog cost exerts considerably more pressure to the unit performance, and hence major maintenance is conducted more frequently to mitigate the presence of defective units. The decrement of the backlog cost leads to the inverse effects (case III). * Variation of the minimal repair cost: With the increment of the repair cost \(C_{R}\) (case VI), major maintenance must be performed more frequently, since the true usefulness of such maintenance is its ability to mitigate the presence of defective units, so the critical age \(A_{0}\)* reduces. Furthermore, we note that at reducing age \(A_{0}\)*, the unit will remain operational for less time, and thus the production threshold becomes less restricted, increasing \(Z_{p}^{*}\) as a countermeasure to ensure enough product availability to satisfy customers' demand. Additionally, product availability is increased by reducing the period of time where the JIT policy is applied, since we note that at increasing \(C_{R}\), the critical age \(B_{JIT}^{*}\) reduces. When the repair cost decreases, we observe the inverse effects (case V). * Variation of the major maintenance cost: The increase of the major maintenance cost \(C_{M}\) (case VIII) is expected to delay the conduction of major maintenance, thus increasing age \(A_{0}\)*. This is because the production unit must attain higher levels of deterioration to justify the expensive cost of a major maintenance. Moreover, the intended consequence of delaying the major maintenance is that the unit will be operational for more time, increasing its responsiveness to customers' demand, and also reducing the need for inventory, decreasing the production threshold \(Z_{p}^{*}\).