# Robust Engineering for the Design of Resilient Manufacturing Systems
## 3 Methods and Tools
### Design of Experiments (DOE)--Taguchi Method  
The procedure that has been followed for the experimental design has been divided into a series of steps which are explicitly presented in the following paragraph. **Step 1:** Setting the objective of the experiment and selecting factors  
In order to investigate the response of a system, the objective should be clearly defined. Subsequently, the parameters affecting the system should be determined. In the following paragraphs of this paper, the parameters are mentioned as factors. Many parameters usually affect the performance value characteristic. However, the most important factors have to be selected so that the analysis complexity will not be increased unreasonably. The parameters are realized as the control factors and are specified freely by the designer. Moreover, the designer is responsible for determining the best values of the control factors. On the other hand, noise factors cannot be controlled by the designer or their settings are difficult or expensive to control. **Step 2:** Level identification for each factor  
The multiple values that are assigned to each factor are called levels. After selecting the number of the factors, the levels of each one should be also determined. This step will be decisive for choosing the suitable Orthogonal Array (OA), which is discussed in the next step, Step 3. Figure 1: Line part simulation of the production. **Step 3:** Standard Orthogonal Array selection  
The number of rows of the OA represents the number of experiments. In order for an array to be a viable choice, the number of rows must be at least equal to the degrees of freedom required for the case study. Similarly, the number of columns of the OA represents the maximum number of factors that can be studied using that array. Usually, it is expensive to conduct experiments, from a computing resources point of view. Therefore, the best practice is to utilize the smallest possible OA that meets the requirements of the case study [37]. The minimum number of experiments that are required for the implementation of the Taguchi method can be calculated based on the degrees of freedom approach, as per the Equation (1). \[N_{Taguchi}=1+\sum_{i-1}^{n}(L_{i}-1) \tag{1}\]  
where,  
\(L_{i}\) stands for the level of each factor and \(n\) for the number of factors. **Step 4:** Selecting the appropriate objective function (Signal-to-Noise ratio)  
The selection of the appropriate objective function for maximization in an engineering design problem is very important since it defines the value of the conclusions about the optimum levels. Usually, in a production line, the target is to maximize the overall  
Figure 2: Flowchart of the proposed simulation model. throughput. This type of problem is referred in the literature as the-larger-the better problem and the corresponding objective function is depicted below. \[n=-10\log_{10}\left(\frac{1}{n}\sum_{i=1}^{n}\frac{1}{y_{i}^{2}}\right) \tag{2}\]  
where,  
\(n\) stands for the Signal-to-Noise ratio (S/N ratio)  
\(y_{i}\) is the response in each experiment \(i\). **Step 5:** Conducting the experiments  
Provided that the control factors (A, B, C, D), the noise factors, the orthogonal array and the objective function have been defined, then the next step involves the execution of the experiments. For each experiment in the OA, the response should be measured and then the S/N ratio must be calculated. Noise factors should also have levels and each experiment will be conducted for different noise factors settings. Afterwards, all the data will be gathered, and the mean value is calculated which in turn represents the system response. **Step 6:** Analysis of means  
The variation caused by each factor to the overall mean is depicted in suitable graphs, where the overall mean is indicated and the average of each factor for every level is also depicted. In order to perform the analysis of means some critical values should be defined at first place.