# Real-Time Maintenance Optimization with Industrial Internet of Things
## 4 Results
### Optimization of Conventional State-Based Maintenance Operations
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**ID** & **Type** & **Child 1** & **Child 2** & **Child 3** & **Child 4** & **Initial State** & **Degradation Rate Parameter** \\ \hline E1 & Entity & & & & 0.980 & \(3.3\times 10^{-2}\) \\ E2 & Entity & & & & 0.985 & \(3.4\times 10^{-2}\) \\ E3 & Entity & & & & 0.950 & \(2.9\times 10^{-2}\) \\ S1 & Serial & E1 & E2 & E3 & & 0.917 & \\ E4 & Entity & & & & 0.992 & \(3.4\times 10^{-2}\) \\ E5 & Entity & & & & 0.960 & \(2.8\times 10^{-2}\) \\ S2 & Serial & E4 & E5 & & & 0.873 & \\ E6 & Entity & & & & 0.994 & \(2.9\times 10^{-2}\) \\ E7 & Entity & & & & 0.990 & \(3.7\times 10^{-2}\) \\ S3 & Serial & E6 & E7 & & & 0.984 & \\ P1 & Parallel & S1 & S2 & S3 & & 1.000 & \\ E8 & Entity & & & & 0.962 & \(3.3\times 10^{-2}\) \\ E9 & Entity & & & & 0.982 & \(3.1\times 10^{-2}\) \\ S4 & Serial & E8 & E9 & & & 0.945 & \\ E10 & Entity & & & & 0.961 & \(3.7\times 10^{-2}\) \\ E11 & Entity & & & & & 0.975 & \(2.6\times 10^{-2}\) \\ S5 & Serial & E10 & E11 & & & 0.937 & \\ E12 & Entity & & & & 0.951 & \(4.1\times 10^{-2}\) \\ E13 & Entity & & & & 0.988 & \(3.7\times 10^{-2}\) \\ E14 & Entity & & & & 0.960 & \(3.6\times 10^{-2}\) \\ S6 & Serial & E12 & E13 & E14 & & 0.902 & \\ P2 & Parallel & S5 & S6 & & & 0.994 & \\ E15 & Entity & & & & 0.986 & \(3.5\times 10^{-2}\) \\ S7 & Serial & P1 & S4 & P2 & E15 & 0.980 & \\ \hline \hline \end{tabular}  
* E: entity, S: serial, P: parallel.  
\end{table} 
Table 3: Parent–child relationships of resources. the impact of maintenance periods on system reliability in three different cases. In our model, we take 20 maintenance periods into consideration. If the length of the maintenance period is 2.6 h, it often occurs that the system's reliability reaches 100%, which suggests that unnecessary maintenance activities were performed, leading to additional costs (see Figure 3). If the length of the maintenance period is 4 h, the system's reliability never reaches 100%. As illustrated in Figure 4, the reliability of the system consistently decreases over time, which suggests that the 4 h maintenance cycle is not optimal for maintaining the system's performance. This extended maintenance period is too long to ensure the system's continuous productivity and efficiency. If the length of the maintenance period is 3 h, it rarely happens that the system's reliability reaches 100%, which indicates that the 3 h long maintenance period is a significantly more cost-effective solution than the more frequent 2.6 h and less frequent 4 h long maintenance periods (see Figure 5). Figure 4: The maintenance period–system reliability function in the case of a maintenance period length of 4 h.  
Figure 3: The maintenance period–system reliability function in the case of a maintenance period length of 2.6 h.  
The other objective is to analyze the number of unnecessary maintenance operations (see Figure 6). It is important, because performing maintenance on a technical device that is in good condition can be counterproductive, as it may lead to unnecessary downtime and increased costs. Over-maintenance can also cause wear and tear on parts that are otherwise functioning properly, potentially reducing the lifespan of the equipment. Furthermore, unnecessary maintenance operations can disrupt the normal (productive) operation and efficiency of the system, leading to a loss of productivity. By examining the impact of maintenance periods on the system's minimum and average reliability, it can be concluded that the more frequent the maintenance, the higher the minimum and average reliability values of the system. The relationship between the maintenance intervals and the system's minimum and average reliability can be modeled using a fifth-degree polynomial with a coefficient of determination value of \(R^{2}>0.99\). This indicates a strong correlation between the maintenance frequency and the system's reliability (see Figure 7). As maintenance intervals decrease, the system's reliability improves, reducing the risk of failures.