## 5 Discussion  
The decision-making of the enterprise is related to the conjoint production and maintenance optimization under quality consideration. The primary aim of the manager is to minimize the total cost of the production process considering the production and maintenance costs and the costs related to the quality. In the industry, the forecasting demands and the service level related to the satisfaction customers are the common points of several companies. Under these various issues, the manager will try to optimize the different costs generated by the production process. So, the manager will try to control the production cadences for each period considering the forecasting demands and the other limits, such as the deterioration, the quality, and the maintenance. In this context, we find the managerial implications of our contribution, which serves to propose an economical production and maintenance policy taking into account the various considerations mentioned before. We present in this paper a solution for this kind of problem, allowing this company, and many other companies with the same kind of problem, to obtain the optimal production planning as well as the optimal maintenance schedule, allowing companies to minimize the total costs. Therefore, the objective is to establish an economical plan of production depending on the random characteristics of the demand, and at the same time, minimize the total cost of production, inventory, and quality. Using Mathematica software, we determined optimal plans of production and delivery quantity (please see Tables 3-5, Tables 8-10 and Tables 11-13). In order to obtain and apply this economical plan, it is necessary that the resources are available and reliable, hence the integration of maintenance strategy on the production system which is used to guarantee the continuity of reliability of the machines by emphasizing the degradation function of the available machine according to its production rate. We used the production and delivery plans to decide the optimal number of PM and the most appropriate maintenance duration when the system is in control and out of control. From the sensitivity analysis (Table 18), we can notice that:  
1. The decrease (respectively the increase) of the inspection cost causes the increase (respectively the decrease) of the sampling interval \(h\) and the decrease (respectively the increase) of the inspection number. In addition, a slight variation in the other decision variables such as the sampling size \(n^{*}\) and \(k_{p}{}^{*}\) was noted. 2. The cost of rejection has a slight influence on the sampling interval and the number of inspections, \(m^{*}\). The decrease (respectively the increase) of the inspection cost causes the decrease (respectively the increase) of the sampling size \(n^{*}\). However, it mainly acts on the proportion of non-conforming units and subsequently on the control limits. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **Variation** & \(n^{*}\) & \(h^{*}\) & \(m^{*}\) & \(k_{p}{}^{*}\) & \(N^{*}\) \\ \hline \multirow{2}{*}{Base} & & 35 & 60 & 144 & 4.6 & 3 \\ \cline{2-7}  & \(-15\) & 40 & 68 & 127 & 4.62 & 3 \\ \cline{2-7}  & +15 & 32 & 52 & 166 & 4.59 & 3 \\ \hline \multirow{2}{*}{\(c_{r}\)} & \(-40\) & 33 & 58 & 148 & 4.4 & 3 \\ \cline{2-7}  & +60 & 39 & 62 & 139 & 4.83 & 3 \\ \hline \multirow{2}{*}{\(c_{F}\)} & \(-20\) & 42 & 72 & 120 & 4.12 & 3 \\ \cline{2-7}  & +20 & 28 & 49 & 176 & 5.8 & 3 \\ \hline \multirow{2}{*}{\(t_{p}\)} & \(-0.5\) & 35 & 59 & 142 & 4.1 & 3 \\ \cline{2-7}  & +0.5 & 36 & 60 & 144 & 4.82 & 2 \\ \hline \multirow{2}{*}{\(n_{pc}\)} & \(-1\) & 32 & 63 & 137 & 3.9 & 4 \\ \cline{2-7}  & +2 & 36 & 55 & 157 & 4.82 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 18: Sensitivity analysis of different parameters. (* denotes the optimal value).