## 2 Methodology  
### Lubrication System Simulation and Component Introduction  
By calculating the distance evaluation factors of various feature parameters, the standard deviation and absolute mean value of the fluctuation signal were selected as the time-domain feature parameters to be used as response covariates in the Weibull proportional hazards model [26]. The lubrication oil system plays a crucial role in diesel engines, effectively reducing friction and wear while extending the machine's service life. It is particularly suitable for large machinery, such as marine engines [27]. In this study, the Chinese Zibo Power Co., Ltd.'s 6210 ZLC/S-2 diesel engine lubrication oil system was selected as the target system for reliability assessment, as shown in Figure 1. A simulation analysis was conducted using the operating time and maintenance strategy of the diesel engine system. The lubrication oil system operates under normal conditions for approximately 29% of the year and undergoes scheduled maintenance once per year. The diesel engine lubrication oil system consists of several critical components, including: the Power Unit Branch (PUB), Generation Unit Branch (GUB), and Protection Device (PD). These components represent critical subsystems that jointly determine the performance and reliability of the lubrication oil system. The lubricating oil power system plays a crucial role in power machinery and equipment by providing essential lubrication, cooling, and safety protection. Its structure primarily consists of three main components: the power unit branch, the generator unit branch, and the safety devices. These components work in coordination to ensure the system's stability, reliability, and long-term operational efficiency. The power unit branch is the core of the lubricating oil power system, primarily responsible for delivering efficient and stable lubrication and cooling for power devices such as steam turbines. By reducing mechanical wear caused by friction and high temperatures during operation, it enhances the overall efficiency of the equipment. Within this branch, the turbine lubricating oil pump serves as a key component, responsible for delivering lubricating oil to various lubrication points while maintaining internal oil pressure balance. This ensures that moving parts operate under an adequate oil film, allowing for smooth and reliable functioning. Additionally, the power unit's lubricating oil cooler facilitates heat exchange and temperature regulation, efficiently reducing oil temperature to prevent performance degradation or equipment damage due to excessive heat. Furthermore, this branch strictly controls oil flow and pressure, ensuring consistent lubrication and cooling effects under varying operating conditions. The generator unit branch primarily serves the power generation system and consists of key components such as the electric lubricating oil pump and the generator lubricating oil cooler. The electric lubricating oil pump acts as an independent lubrication power source for the generator set, ensuring a stable supply of lubricating oil to critical high-precision rotating components, such as the generator rotor and bearings. This reduces frictional losses and enhances both operational efficiency and equipment lifespan. During generator operation, the continuous variation in electrical load and mechanical friction leads to an increase in oil temperature, which may compromise lubrication performance and system reliability. To address this, the generator lubricating oil cooler utilizes an efficient heat exchange structure to lower the oil temperature and maintain internal thermal stability. This ensures that lubrication conditions remain optimal throughout operation. The safety module is a critical safeguard in the lubricating oil power system, comprising components such as the oil return valve, elevated oil tank, and safety pressure relief valve.