# Robust Engineering for the Design of Resilient Manufacturing Systems
## 3 Methods and Tools
### Simulation Model  
Referring to the actual production line, the procedure begins with the arrival of the raw material, namely the copper billet. The next step is the extrusion press where the billet subjects to 40,000 kN force. The extruded tubes are called mothertubes. Mother tubes undergo a series of dimensional reductions from this point and forward. For the final product, the number of demotions that are required is varying according to orders placed by the customers. Following, the production line is split into two routes where the first one refers to the drawback and the second one to the cold pilger mill. In these two machines, the first demotions are performed. Next, the tubes are inserted into the spinner blocks. These machines are responsible for the higher percentage of the dimensional reductions in the production line. For example, an original tube diameter could be 35 mm and the final diameter 9.5 mm in or 6.35 mm. After the spinner blocks, the parts are directed to the final formatting machines in order to take the final form, for example, inner helix or coating, according to the order specifications.  
As far as planning strategy is concerned, the MTO philosophy dominates. Although the manufacturer offers a defined variety of products, production profile is based on customers' orders. This strategy entails to limited buffers among the workstations and also a high dependency of the machines. Due to the high processing capabilities of the spinner block machines, specifically about 1200 m/min linear velocity and phase change less than one minute.  
The manufacturing system, i.e., the copper tube production, has certain unique features that need to be considered during the modelling process. The manufacturer may offer a wide variety of different products, and specifically more than 1000 different products, which are inefficient to model, therefore they are omitted. It should be clear that not all parts of the production line are being simulated. Instead, only a certain portion of production line is modelled, in order to judge easily and quickly the response to various factors' change since indeed, a simulation model is supposed to be an abstraction and simplification of reality [36]. In collaboration with the production experts, the products were divided into eight groups (A-H) and the model of the production depicted in Figure 1 was created.  
A simulation model of a complex system can only be an approximation to the actual system, so as to ensure that the model is not unnecessary complex [36]. Towards this end, an adapted production model was created in collaboration with the experts that simplifies the current production. The simulation model is validated to ensure the credibility of the results that will emerge from the experiments. The DOE in order to limit the simulation effort is executed and last but not least, experiments are conducted so useful conclusions can arise and assist the decision-making process towards the goal of production maximization. The flowchart of the simulation model is presented in Figure 2, while the development is taking place in Section 4. The five final machines, as they termed before, are referred as \(M_{i}\) where \(i\) ranges from 1 to 5.