# Robust Engineering for the Design of Resilient Manufacturing Systems
## 3 Methods and Tools
### Simulation Model  
The developed simulation model as well as the routing of the parts within the production line are presented and discussed in the following paragraphs. The simulation time is measured in hours, taking into consideration that the objective of the current study is the maximization of the annual throughput. The product groups and the physical product, which is the so-called mothertube, are considered as input to the model. The Machines for PNC products are M\({}_{1}\) and M\({}_{2}\) and for LWC products are M\({}_{3}\), M\({}_{4}\), and M\({}_{5}\). Initially, the physical part, which considered to be the copper billet of 500 kg, is represented by the part named \"Mothertube\" and appears on the model with interarrival time 0.067 h, namely 4 min. The second part for beginning the simulation is the part \"A, B, C, D, E, F, G, H\" and their interarrival time is 168 h, as indicated by the company, while the product mix is formulated through the pre-described datasets that are resulted form the real data since they represent the orders placed from the customers. Further to that, transportation times between some workstations were defined by the production engineers of the company. The simulation model includes several entities which represent either a process or a piece of equipment/machine tool in the production line. each block shown in Figure 5 is referred and explained in detail below. Each \"Mothertube\" is combined with a demand part in the \"Orders\" block. The goal of this block is to combine the mothertube, which is produced under the \"Push\" approach with the corresponding order, in order to simulate the \"Pull\" approach hereafter. It is stressed out that the \"Orders\" block does not induce any time delays in the flow of the model. This technique is used in order to assign different characteristics to every product group such as processing time, transportation speed, and also for simulating the demand and the arrival of the physical product. Each product group can be processed in particular machines and the routing is constraint by the standards set by the companies. Starting from the front stage of production, namely the drawbench (\"DB\") as well as the pilger mill (\"PM\"), the routing illustrated in Table 4.  
Whenever a product group can be processed by both machines in order to decide where it should be stored, it is given priority to the buffer that has a smaller number of parts so there will be a balance between the processing parts in each machine for avoiding the congestion and utilizing properly the equipment. The routing stage is followed by the drawbench and the cold pilger mill, which in the simulation model are represented by the \"DB\" and \"PM\" machines respectively. Their production rate is derived from the same normal distribution for all the products at this level. The value of processing time is 0.083 h and 0.347 h per part respectively. Following the spinner blocks, machines that are responsible for the main demotions in the product are represented as \"Spinner Block\". Three identical spinner blocks have been included while their processing time is following the normal distribution, according to the data analysis and it varies among the groups. the final stage in the simulation model involves the five machines for shaping the final product and their graphics are depicted as M\({}_{1}\), M\({}_{2}\), M\({}_{3}\), \begin{table}
\begin{tabular}{c c c} \hline
**Group** & **Drawbench** & **Pilger Mill** \\ \hline A & Yes & No \\ \hline B & Yes & Yes \\ \hline C & Yes & No \\ \hline D & No & Yes \\ \hline E & No & Yes \\ \hline F & Yes & Yes \\ \hline G & Yes & Yes \\ \hline H & Yes & No \\ \hline \end{tabular}
\end{table} 
Table 4: Routing regarding drawback and pilger mill. M\({}_{4}\), and M\({}_{5}\) in Figure 5. The two latter machines, i.e., M\({}_{4}\) and M\({}_{5}\) are assigned to process only PNC products as long as the rest are processing explicitly LWC and their cycle time is following the LogNormal, normal, or gamma distribution based on the product group.