# Life Cycle Cost Estimation and Analysis of Transformers Based on Failure Rate
## 2 Materials and Methods
### Failure Tree Analysis  
Failure tree analysis (FTA) is a systematic and quantitative risk assessment and reliability analysis method mainly used in engineering, aerospace, nuclear energy, chemical, healthcare, and other fields to identify and evaluate the likelihood and risks of potential failures, accidents, or events within a system or process [23]. Failure tree analysis is typically applied to study complex systems or processes where significant events or accidents may occur. These events can be equipment failures, safety incidents, system failures, and so on.  
In failure tree analysis, basic events are irreducible events that serve as the starting points for the analysis. Basic events can represent specific failure modes, failure conditions, or the occurrence of a particular event. Failure trees are represented using a tree-like structure where the root node represents the event of interest (e.g., system failure), and branches depict various possible pathways leading to that event. The relationships between pathways are described using logical gates such as AND gates (indicating that all branch events must occur) and OR gates (indicating that at least one branch event must occur) [24]. FTA is used not only for qualitative analysis but also for quantitative analysis. By assigning probabilities or probability distributions to each basic event, it is possible to calculate the probability of a specific event occurring within the system or process. This helps assess system reliability and risk. Through the analysis of the failure tree, it is possible to assess the risk level of specific events within the system or process. This aids in identifying potential risk factors and taking preventive measures to reduce or eliminate these risks.  
The failure mode analysis method analyzes various failure situations of all components that make up the system one by one and determines their impact on the entire system [25]. The failure severity analysis method is a support for the failure mode analysis method, which comprehensively considers the failure rate and corresponding failure consequences of a failure to evaluate the degree of harm of a certain failure mode. Failure tree analysis collects a large number of failure relationships and analyzes the causal relationships of events from top to bottom, establishing a logical AND/OR relationship between events and ultimately establishing a failure analysis structure. Failure tree analysis is widely recognized as a simple, effective, and most promising method in safety and reliability engineering [26].  
Figure 2: Composition of the life cycle cost for power grid equipment.  
The main research content of this article is to draw the corresponding distribution of transformer failure rate through more accurate estimation of transformer failure rate, so as to determine the maintenance interval of the transformer based on the transformer distribution map and further calculate the corresponding full life cost of the transformer. Finally, a more accurate estimation of the life cycle cost can be obtained to assist in transformer selection during substation construction arrangement of transformer maintenance and determination of the optimal retirement period for transformers.