# Robust Engineering for the Design of Resilient Manufacturing Systems
## 4 Results
The analysis of variance supposing zero error term is executed using Equation (9) as it is apparent in Table 10.  
The contribution percentages are depicted in Figure 7. The values above resulted from the formulas on the corresponding methodology section and the factor with the greater impact is the \"interarrival\" with 62.1% effect on the throughput as it was indicated by ranking in the analysis of means. However, an approximate estimate of the error variance can be obtained by pooling the sum of squares corresponding to the factors having the lowest mean square. As a rule of thumb, the sum of squares corresponding to the bottom half of the factors corresponding to about half of the degrees of freedom be used to estimate the error mean square or error variance. In this case, the factors B, C are selected as they have the lower mean square value. This manner of error variance computation is called pooling. The results from the pooling operation are presented in Table 11. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \
\begin{tabular}{c} **Degrees of** \\ **Freedom** \\ \end{tabular} & **Sum of Squares** & **Mean Square** &
\begin{tabular}{c} **Contribution** \\ **Percentage** \\ \end{tabular} \\ \hline Interarrival Time & 2 & 14.8232062 & 7.41160312 & 62.10347579 \\ \hline Buffer Capacity & 2 & 3.33065625 & 1.66532812 & 13.95415582 \\ \hline Number of final & 2 & 0.56660625 & 0.28330312 & 2.373860077 \\ \hline Number of & 2 & 5.16860625 & 2.58430312 & 21.65445233 \\ \hline Error & 0 & 0 & & \\ \hline Total & 8 & 23.8685614 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: ANOVA table excluding error. Figure 7: Contribution of each factor according to ANOVA table. The calculation of error variance for this case is calculated as follows:  
\[\sigma_{e}^{2}=\frac{3.8973}{4}=0.974315625\]  
The inferences that arise from this procedure are that having control over the interarrival time has a great impact on the throughput. The number of spinner blocks is considered as a secondary factor which has an impact of about 21.6% on the throughput. It should be clarified that this is not an analysis that provides accurate results of the system, especially when it changes dynamically, but offers to the designer the capability of identifying the main contributors in the performance value and have a prompt inspection on the system. Towards the purpose of validating the simulation model, so the results can be credible and measurable, at first place, the deterministic data from the company inserted into the model and then the comparison between the deterministic and the stochastic model is carried out. The comparison is performed between the two models in order to find the error inserted when assuming a normal distribution for describing the arrival times. The model was simulated for one-year runtime, which is equal to approximately 8600 h.  
As it has already been stated, the aim of this research work is to further increase the throughput of the manufacturing system based on the utilization of real data. To that end, calculations on the Signal to Noise ratio by posing as a criterion the bigger the better in order to achieve the highest total parts production were done. After that, experiments were conducted for What-If scenarios and the output was maximized (44,000 coils). Moving on, we have used the advanced experimenter mode of the simulation tool and experiments were done for different values of the interarrival time for the two main product categories. The purpose was to find the best combination of interarrival times. Moreover, this was done to achieve high utilization of the machines, maximum number of produced parts and low Work-In-Process (WIP) at the same time. Finally, with the implementation of this method, the cooper industry managed to produce 3000 more products in comparison with the current production model.\"  
Multiple runs have been performed for the evaluation of the proposed methodology. The overall result for the evaluation is taken as the mean of the results for each run.