## 2 Related Works
### Periodic Imperfect Maintenance to Minimize Maintenance Costs
proposed an opportunistic conditional maintenance strategy for electrical distribution systems (EDSs) based on the structural dependency problem of power equipment, aiming to maximize the reliability of EDSs while reducing maintenance and troubleshooting costs [27]. [PERSON] et al. optimized power system maintenance strategies through a genetic algorithm, solving the trade-off problem between system maintenance risk and potential system fault risk [28]. [PERSON] et al. designed an optimal preventive maintenance algorithm based on the update reward theorem, optimizing the maintenance plan of wind turbines and reducing maintenance costs [29]. [PERSON] et al. introduced variable weights based on lifecycle cost and retirement age to select the optimal maintenance strategy for power transformers [30]. [PERSON] et al. proposed a dynamic group maintenance strategy based on imperfect maintenance models, considering the economic dependence between wind turbines in wind farms [31]. [PERSON] et al. proposed a transformer maintenance method based on health index assessment, helping maintenance personnel conduct early fault diagnosis and reduce maintenance costs [32]. [PERSON] et al. introduced a two-stage framework for alternative planning, optimizing asset intervention planning using a Monte Carlo program based on the probabilistic health index (HI) method [33]. [PERSON] et al. developed an optimization model of maintenance strategy for large-scale hydropower stations, considering multi-objective and multi-standard structures of complex equipment [34]. [PERSON] et al. proposed a dynamic preventive maintenance strategy for subway vehicle traction systems, incorporating service age-decreasing factors and failure rate-increasing factors into a new dynamic reliability model [35]. Our comprehensive analysis of recent literature on periodic imperfect maintenance planning in the power industry reveals several trends and opportunities for improvement. We evaluated these studies based on three critical aspects: consideration of small sample scenarios, dynamic maintenance factors, and dynamic maintenance costs. The results of this analysis are presented in Table 1.  
As evidenced by Table 1, while current research in periodic imperfect maintenance often focuses on precise descriptions of effective age, there remain significant areas for enhancement. We have identified three key aspects that warrant further investigation:  
1. Dynamic increase in maintenance costs: Most studies prioritize optimizing lifespan extension and maintenance intervals through factors like effective age, overlooking the temporal variability of maintenance costs. For power transformers, the escalating failure rates with each maintenance cycle inevitably lead to increased costs in subsequent maintenance periods. This dynamic cost structure is often neglected in current models. 2. Limited maintenance history data: The scarcity of defect samples in long-lifespan products like power transformers poses a significant challenge. Many studies fail to address the practical difficulties engineers face when planning maintenance for such equipment with limited high-quality historical data. 3. Variability of imperfect maintenance improvement factor: Current research often assumes a constant degree of imperfect maintenance or focuses on minimal maintenance scenarios. However, for power transformers, the efficacy of each maintenance task varies over the equipment's lifespan, a nuance that is frequently overlooked in existing models.