# Designing of Machine Backups in Reconfigurable Manufacturing Systems
## 3 Results
However, it is necessary to find out the changed machine classification for the transformed operating stages for this newly designed configuration. From this point of view, it is necessary to use the assignment submodule, which will be used again even after defining the device backup. We can calculate the average values of the parameters defined for the operating stage for specific machines based on this approach. Information about the assigned machines from the assignment submodule will be used to calculate the average values. Therefore, the resulting average values are calculated using Formulas (6)-(12). From the results obtained, shown in Table 3 below (note the line marked in grey represents the lowest utilization factor \(K_{vi}\)), it is possible to calculate the utilization factor for each operating stage. We calculate the utilization factor using the Formula (13). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Production Stages (i)** & \(\mathbf{r_{n_{i}}}_{\text{freq}}\) & \(\mathbf{\theta_{i_{i_{i_{i_{i_{i_{i_{i_{i_{i_}}}}}}}}}}}\) & \(\mathbf{w_{a_{i_{i{i_{i{i_{i_{i}}}}}}}}}\) & \(\mathbf{\tau_{a_{i_{i{i_{i{i_{i}}}}}}}}\) \\ \hline
1 & 1.1429 & 2.1875 & 3 & 0.72917 \\
2 & 1.1429 & 2.1875 & 3 & 0.72917 \\
3 & 0.9372 & 4.9793 & 5 & 0.99587 \\
4 & 0.9372 & 4.9793 & 5 & 0.99587 \\
6 & 0.9372 & 5.6907 & 6 & 0.94844 \\
7 & 0.9372 & 4.2680 & 5 & 0.85360 \\
8 & 1.4451 & 4.4980 & 5 & 0.89960 \\  & & 4\({}_{r_{r}}\) & 38 & & \\ \(K_{p}\) & 1.00 & 1.02 & 1.04 & 1.06 & 1.08 & 1.10 & 1.12 & 1.14 & 1.16 & 1.18 \\ \(q_{n_{p}}\) (pcs) & 38 & 40 & 40 & 42 & 42 & 42 & 43 & 43 & 43 & 44 \\ \(n_{z}\) (pcs) & & & & & & & & \\ \(n_{sp}\) (pcs) & 972 & 989 & 989 & 1005 & 1005 & 1038 & 1038 & 1038 & 1067 \\ \(n_{z}\geq ns_{p}\) & no & no & no & no & no & no & no & no & yes \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Initial configuration and simulation model verifications. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Production** & \(\mathbf{\lambda_{i}}\) & \(\mathbf{\mu_{i}}\) & \(\mathbf{T_{i}}\) & \(\mathbf{\Phi_{i}}\) & \(\Sigma(\mathbf{U_{f-g}})_{i}\) & \(\Sigma(\mathbf{D_{f-g}})_{i}\) & \(\mathbf{P_{p_{i}}}\) & \(K_{vi}\) \\
**Stages (i)** & **(min.\({}^{-1}\))** & **(min.\({}^{-1}\))** & **(min.)** & **(min.)** & **(min.)** & **(min.)** & **(min.)** & **(min.)** & **(P_{p_{i}}\)** & \(K_{vi}\) \\ \hline
1 & 0.0239 & 0.0339 & 41.9048 & 29.5238 & 586.6667 & 413.3333 & 14 & 0.5867 \\ \hline
2 & 0.0403 & 0.0215 & 24.8095 & 46.6190 & 347.3333 & 652.6667 & 14 & 0.3473 \\
3 & 0.0313 & 0.0254 & 31.9857 & 39.4429 & 447.8000 & 552.2000 & 14 & 0.4478 \\
4 & 0.0278 & 0.0511 & 35.9778 & 19.5778 & 647.6000 & 352.4000 & 18 & 0.6476 \\
5 & 0.0270 & 0.0459 & 37.0588 & 21.7647 & 630.0000 & 370.0000 & 17 & 0.6300 \\
6 & 0.0478 & 0.0375 & 20.9206 & 26.6984 & 439.3333 & 560.6667 & 21 & 0.4393 \\
7 & 0.0148 & 0.0174 & 67.4500 & 57.5500 & 539.6000 & 460.4000 & 8 & 0.5396 \\
8 & 0.0403 & 0.0359 & 24.7895 & 27.8421 & 471.0000 & 529.0000 & 19 & 0.4710 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Utilization factors. From the results, it can be concluded that the lowest value of the utilization factor is reached by production stage 2. Therefore, it will be necessary to design a machine backup for this workplace. The machine can be backed up in a cold or warm state. The type of deposit can be decided based on comparing the values of the coefficients of use of cold and warm backup. First, we calculate the utilization factor for the cold backup using Formulas (14)-(16). The following is the calculation of the value of the warm backup factor, in which formulas will calculate (17)-(19). However, the above calculations for the cold deposit do not contain the onset time \(\Delta_{tz_{i}}\) and their value is therefore not relevant. For this reason, it is necessary to determine the rise time of the backup machines and recalculate the resulting value of the cold backup with the calculated rise time.