# Life Cycle Cost Estimation and Analysis of Transformers Based on Failure Rate
## 3 Results  
### Failure Rate Analysis  
Through data analysis, we have learned that many power companies still use a more frequent regular maintenance mode. Regular maintenance itself does not consider the condition of power equipment, including its own condition and the surrounding natural environment, and only arranges regular maintenance of transformers based on historical data over the years [27]. Disoperation by personnel during the maintenance process can easily cause damage to the transformer, which may lead to a decrease in the service life of the transformer. Moreover, due to the blindness of regular maintenance, it is easy to waste manpower and financial resources [28]. At present, the power grid is in a stage of rapid expansion and the quality of the corresponding first-line inspection personnel of the power company is still uneven, with fewer excellent first-line inspection personnel. Based on the above reasons, it is necessary for enterprises to change their previous regular maintenance mode to condition-based maintenance mode. The development of condition-based maintenance requires the progress of online monitoring and diagnosis technology, and the reasonable evaluation of transformer status. Therefore, the analysis and estimation of transformer failure rate is particularly crucial. Accurate analysis of transformer failure rates and prediction of future transformer failure rates can enable power companies to arrange inspection personnel in a timely and reasonable manner, saving a lot of unnecessary inspection costs, and manpower and resources [29]. At the same time, accurate analysis of the transformer failure rate can reasonably plot the distribution of the transformer failure rate over time, which provides a technical basis for introducing life cycle cost management and operating transformers [30]. In this study, based on the fitted distribution of transformer failure rates, the maintenance and failure costs of the transformer throughout its entire life cycle are estimated. In this study, we combined other scholars' classification methods for transformer failures and followed the analysis steps and principles of failure trees. Considering the vulnerability areas of transformers, it treats the occurrence of transformer failures as the top event, denoted as \"T\". The transformer failures are categorized into several major types, including lead failures, winding failures, bushing failures, on-load tap changer failures, cooling system failures, protective device failures, and core failures, totaling seven major categories [31]. For these seven major failure categories, further subdivisions are made based on the structural characteristics of various components. Failure events that cannot be subdivided further are referred to as the bottom events of the failure tree. After analyzing and obtaining all these events, a transformer failure tree is established based on the logical relationships between them. The occurrence of each bottom event will lead to the occurrence of intermediate events, and the occurrence of each intermediate event will lead to the occurrence of top events. Therefore, the logical relationship of each level of event is an AND gate relationship, that is, the occurrence of each bottom event will lead to the occurrence of its top event. Finally, the logical relationship of each event in the failure tree is obtained, resulting in the schematic diagram of the failure tree shown in Figure 3.  
In reliability engineering, there are various models that describe the failure rate of electrical equipment, and commonly used models include the exponential model, normal model, will model, etc. According to statistical analysis, it can be seen that the transformer has just been put into operation. There will be a brief period of high failure rate during use, followed by a period of over 10 years of maintenance. In a low failure rate operating state, the failure rate has been increasing exponentially year by year.