# Optimal Maintenance Schedule for a Wind Power Turbine with Aging Components
## 8 Conclusions and Future Work  
This paper introduces a new optimization algorithm relying on the renewal-reward theorem. In the multi-component setting, a new concept called the virtual replacement is introduced, allowing us to treat each replacement event as a renewal event, even when some components are not actually replaced with new ones. The new algorithm is illustrated by careful simulation studies in the framework of a four-component system of a wind turbine, searching for optimal maintenance plans under various initial conditions.  
In sensitivity analysis 1, we conducted a detailed study on the replacement cost of a single component based on its age \(a\) at a potential replacement moment \(t\). Our findings indicate that the replacement cost of the component increases as the parameter \(a\) increases. For the component with \(a\) below a certain critical value, the component is deemed to be in a sufficiently good condition to not require a replacement. However, when the age \(a\) exceeds the critical value, the optimal solution is to plan for a PM activity at the time \(t\).  
Sensitivity analysis 2 examines the influence of the crucial parameter m representing the monthly value depreciation of a generic wind turbine component. Our results show that as m increases, the optimal PM time for the component also increases. When m is large enough, the optimal solution is to never perform the PM activity.  
Sensitivity analysis 3 deals with the effect of the starting time \(s\) of the scheduling period \([s,T]\). For a single-component system, we have observed that as long as \(s\) is not  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(d=1\) & **1** & **2** & **3** & **4** & **Monthly Maintenance Cost** & **CPU Time** \\ \hline NextPM & x & x & 43 & x & 4.731 & 49 s \\ New algorithm & x & x & 43 & x & 4.703 & 2 s \\ \hline \(d=5\) & **1** & **2** & **3** & **4** & **Monthly Maintenance Cost** & **CPU Time** \\ \hline NextPM & 50 & 50 & 50 & 50 & 4.964 & 54 s \\ New algorithm & 51 & 51 & 51 & 51 & 4.881 & 2 s \\ \hline \(d=10\) & **1** & **2** & **3** & **4** & **Monthly Maintenance Cost** & **CPU Time** \\ \hline NextPM & 52 & 52 & 52 & 52 & 5.061 & 55 s \\ New algorithm & 52 & 52 & 52 & 52 & 5.040 & 2 s \\ \hline \hline \end{tabular}
\end{table}
Table 3: A comparison of the earlier NextPM algorithm and the algorithm of this paper.  
too close to \(T\), the optimal solution is to perform a PM when the component in question reaches a certain critical age.  
Case study 1 estimates that compared to the pure CM strategy, our optimization algorithm on average saves around 30% of the maintenance costs. In case study 2, we compared our new algorithm with an earlier algorithm NextPM from [7]. The study demonstrates that the new algorithm yields precise outcomes while significantly reducing CPU processing time. Compared to the NextPM algorithm, our new algorithm has the advantage of being able to handle age-dependent PM costs.  
The algorithm of this paper can handle only replacement maintenance activities. In the future, it would be worthwhile to study how other maintenance activities, such as inspection and minor or major repair, affect the optimal PM scheduling plan. Another interesting development would be to consider the case in which the PM replacement cost is a non-linear function of the component's age. Finding the optimal PM scheduling plan in this case is an interesting and challenging problem.