# Real-Time Maintenance Optimization with Industrial Internet of Things
## 4 Results
### Optimization of Conventional State-Based Maintenance Operations  
The analyzed production system includes 15 entities. In this case, study, these entities represent machine tools and assembly stations. Although the resources responsible for material handling and transportation are not marked separately, the case study explains how to take them into account. The entities within the production system are connected in both serial and parallel configurations, which defines the structure of the production process. Figure 2 shows the structure of the analyzed production system. The mathematical description of the structure (layout) of the production system is defined as shown in Table 3. Table 3 defines parent-child relationships according to the recursive method described in the previous section. Table 3 also shows the basic degradation rate, which is a function of operation time. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Hyper Parameter** & **Description** & **Value** \\ \hline Use multiple starting points & Enables global search by starting from multiple initial guesses & Disabled \\ Population size & Number of different initial guesses used if & 100 \\  & multistart is enabled & \\ Random seed & Seed value for random number generation & 0 \\  & (for reproducibility) & \\ Require bounds on variables & Ensumes each decision variable has upper and lower bounds when using multistart & Enabled \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 2: Structure of the analyzed production process. We modeled the state of each entity using an exponential distribution. This choice is widely used in production system simulation studies due to its simplicity. The exponential distribution assumes a constant failure or transition rate, which is a reasonable approximation for many technical systems during their useful life phase. It also allows for the efficient simulation of random events such as failure times, repair times, time between breakdowns, service times, arrival times in queues, system response times, component lifetimes, and inter-arrival times in Poisson processes. By applying this model, we can realistically capture the stochastic behavior of the system without introducing unnecessary complexity. In both numerical studies (simulation), we have chosen the following parameters for the calculation of the value of the objective function:  
* the initial income generated by the production operations of the production system: \(c_{SYS}^{PROD}=2000\) USD
* the initial maintenance cost: \(c_{SYS}^{MAIN}=1200\) USD
* influencing factor, which defines the characteristics of the relationship between the reliability and the income, depending on the productivity: \(\theta=0.5\)
* influencing factor, which defines the characteristics of the relationship between the length of the maintenance period and the specific maintenance costs: \(\varepsilon=0.1\). If maintenance is performed at regular intervals, one of the most important optimization parameters is the selection of the optimal maintenance intervals. Based on the mathematical model outlined in the previous section, it is possible to determine the optimal maintenance intervals in the current case study as well. Regular maintenance helps improve the reliability and overall performance of the system. Therefore, choosing the right maintenance frequency can significantly impact system efficiency. Let us examine how system reliability changes over time. The goal is to evaluate how different maintenance intervals affect the overall reliability of the system during this period. We have examined