## 6 Multi-Scenario Analysis  
In this section a general multi-scenario analysis is developed, considering the effect of the automatic reconfiguration of a smart self-adaptive prototype (as in Configuration #2.2) toward the manual reconfiguration (as in Configuration #2.1). The aim of this analysis is to prove the potential cycle time saving achievable by implementing such systems, as described in the proposed framework in Section 3. The parameters included in the analysis are in the following, while their range of variation and/or specific values are in Table 7.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Values** & **Measurement Unit** \\ \hline MT & [60: 60: 1800] & Sec/pc \\ ART & [1 5 10 15 20] & Sec/reconfiguration \\ RN & [0:1:100] & integer \\ M\% & [0:25:100] & \% \\ \hline \hline \end{tabular}
\end{table}
Table 7: Range of variation of the input parameters.  
Figure 9: Variations along the \(z\)-axis of the right hand for (**a**) Configuration #1 and (**b**) Configuration #2.  
RN: (number of reconfigurations) during the cycle time [# reconfigurations/cycle time] * M%: (average masked time percentage) of the SASAS reconfiguration during the assembly tasks performed by the operator [%]. For SASAS prototype with manual reconfiguration M% = 0, while, in the case of automatic reconfiguration and complete collaboration, M% = 100. The numerical analysis assesses, as a function of the input parameters, the following output. Output * CTmr: (cycle time with manual reconfiguration) of the SASAS prototype (as in Configuration #2.1) [sec/pc] evaluated as: \[\text{CTmr}=\text{MT}+\text{ART}\cdot\text{RN}\] (2) * CTar: (cycle time with automatic reconfiguration) of the SASAS prototype (as in Configuration #2.2) [sec/pc] evaluated as: \[\text{CTar}=\text{MT}+\text{ART}\cdot\text{RN}\cdot(100-\text{M}\%)\] (3) * DELTA: (gap percentage of the cycle time between the two configurations) of the SASAS prototype evaluated as in Equation (4). \[\text{DELTA}=\frac{\text{CTmr}-\text{CTar}}{\text{CTar}}\;[\%]\] (4)  
To perform the multi-scenario analysis, values of MT between 60 and 1800 sec/pc (step equal to 60 s) are considered. The number of reconfiguration varies from 0 to 100 (step equal to 1) and each reconfiguration takes from 1 to 20 s (step equal to 5 s). Finally, the average masked time percentage ranges from 0 to 100% (step equal to 25%). The main results are summarized in Figures 10 and 11.  
Figure 10 shows the ANOVA analysis of the input values versus DELTA. The main effect plot demonstrates that the mounting time MT does not affect the result. On the other hand, it shows a positive influence of ART and RN with a less than linear behavior, while M% has a direct positive linear influence. The average cycle time reduction moving from manual to automatic reconfiguration ranges from 0 to more than 20%.  
Figure 10: Main effect plot of gap percentage of the cycle time between the two configurations (DELTA) versus mounting time (MT), average reconfiguration time (ART), number of reconfigurations (RN), average masked time percentage (M%).  
Considering ART = 5 s, as in the experimental analysis of the proposed SASAS prototype, Figure 11 shows the DELTA trend versus M% and RN for the considered MT range of variation. The contour plot in Figure 11 shows a hyperbolic trend according to the two input parameters, with a potential saving that can reach 40% of the entire cycle time.  
Considering more than 75.000 scenarios, this multi-scenario analysis generally tests the concept of A3 Ss with automatic reconfiguration, showing the potential benefits in terms of cycle time-saving.