## 1 Introduction
First, system reliability is computed on the basis of the failure rate of components. However, in the system design stage prior to system manufacturing, because failure data in practice are limited, the designers' cognition of component failure rate must be inaccurate and inadequate, which is manifested as epistemic uncertainty [8; 22]. In order to capture this uncertainty, it is more effective to treat the component failure rate as a random variable [23; 24], rather than the average failure rate achieved by the designers' own experience combined with the historical failure data of the same type of component [25; 26]. Second, the operating environment of aircraft is variable, so even for aircrafts of the same type, their service history and stress-bearing process are bound to be different, leading to obvious dispersion in the failure occurrence of different aircraft individuals, which is manifested as the uncertainty of failure [22]. Mathematically, that is, although the Bath-Tub curve shows that the mean time to failure (MTTF) of each component in the system is a constant during accidental failure period (operation stage of the system) [27], it is a statistical concept based on a large number of failure time samples of the same type of components; furthermore, the fact is that the failure time of each component of the same type is generally different in practice [28; 29], and the failure rate of each component is the reciprocal of the MTTF value, which means that the failure rate of each component is also a statistical average value of the failure rates of different components of the same type; therefore, for different component individuals, their true failure rates should be different, and the calculation of system reliability under the premise of the constant failure rate of components will only quantify the average performance of the same type of aircraft system in reliability, but cannot help designers to fully measure all possible performance of this type of system in reliability [30]. For each aircraft, not only is the cost of manufacturing, operation, and maintenance extremely high, but it is also related to the safety of a large number of passengers. Therefore, it is more and more difficult to meet the reliability requirements of passengers, airlines, and other stakeholders by just using the component average failure rate to assess system reliability [31]. In light of the above problems, in recent years, researchers have begun to break the assumption that the component failure rate is constant and gradually treat component failure rate in AEPS as a random variable that obeys a certain distribution. [PERSON] et al. [32] proposed quantifying the uncertainty of component failure rate based on expert experience, and in further qualifying the uncertainty of the system level through the probability distribution curve of power supply reliability. [PERSON] et al. [33] and [PERSON] et al. [34] proposed the concept of the optimal probability distribution of the component failure rate based on cross entropy theory, and used the power supply system of a multi-electric aircraft as an example to apply this method to the uncertainty analysis of power supply reliability. To reduce the size of conditional probability tables, [PERSON] et al. [35] provided an improved dynamic Bayesian network modeling method that combined two-way reasoning to perform reliability analysis and fault diagnosis of a power supply system. [PERSON] et al. [36] considered the influence of changes in the working environment of aircraft on the failure rate of components, developed a method to quantify the uncertainty of the component failure rate, and presented a three-level model for computing power supply reliability under different working environments.