## 5 Case Study  
### Case Calculation and Analysis  
The forced oil circulation cooling system, a critical element of power transformers, comprises five main components: fan, control box, cooler, heat sink (tube), and submersible pump. Due to the negligible occurrence of defects in the heat sink (tube) over the nearly 30-year record period--with only one general defect that can be fully addressed duringoverhauls--we exclude this component from our analysis. Our optimization efforts focus on the maintenance intervals for the fan, control box, cooler, and submersible pump. Based on the user-provided data for the forced oil circulation cooling system and its acceptable level of unreliability, we conducted a comprehensive analysis involving data collation and failure rate conversion. The results of this analysis are presented in Table 3. Currently, the system operates on a uniform maintenance interval of 720 h (equivalent to 30 days). Our analysis reveals significant discrepancies in component reliability under this maintenance regime:  
1. Some components, such as the control box with serious defects, exhibit failure rates substantially below the acceptable threshold. This suggests potential over-maintenance, leading to unnecessary resource expenditure. 2. Conversely, other components, notably the fan with serious defects, demonstrate failure rates exceeding the acceptable limits. This indicates insufficient maintenance under the current interval, potentially compromising system reliability and failing to meet industry standards. These findings highlight a critical imbalance in the current maintenance strategy. The 720-h uniform interval approach fails to account for the diverse reliability characteristics of individual components, resulting in both over-maintenance and under-maintenance scenarios within the same system. Consequently, we conclude that there exists substantial room for optimization in the maintenance planning of the forced oil circulation cooling system. A more nuanced, component-specific approach to maintenance intervals could significantly enhance overall system reliability while potentially reducing unnecessary maintenance activities and associated costs. This optimization opportunity underscores the need for a more sophisticated, data-driven maintenance strategy that aligns more closely with the specific reliability profiles of each component within the system. Utilizing the systematically organized data from the forced oil circulation cooling system, we first estimated the severity of defects for each component using Weibull distribution parameters. The results of this fitting and testing process are presented in Table 4, with the corresponding probability density distributions (PDFs) of faults illustrated in Figure 6. Analysis of the distributions in Figure 6 reveals several key insights:  
1. Component similarity: The majority of components exhibit remarkably similar distributions across different severity levels. This similarity suggests that these components share comparable temporal failure characteristics, with a propensity for failures to occur in the early stages of operation. This finding has significant implications for maintenance cycle planning, as it allows for the potential coordination of maintenance activities across multiple components, thereby reducing unnecessary interventions and optimizing resource allocation. 2. Anomalous behavior: Despite the general trend, a small subset of components, notably the cooler (as depicted in Figure 6c), demonstrates significant deviations in their distribution patterns under critical conditions. These deviations are particularly pronounced when compared to the distributions observed for common and severe defects. 3. Cooler-specific insights: The distribution curve for critical defects in the cooler exhibits a distinct right-skew, approximating a normal distribution. This characteristic suggests that critical defects in the cooler tend to manifest later in the operational lifecycle.