## 1 Introduction  
The aircraft electrical power system (AEPS) is a system that provides electrical energy for equipment related to flight safety such as navigation, control, and communication. Once a failure occurs, it will often cause huge property losses and even casualties [1, 2]. For example, in January 2013, Boeing 737 experienced failures two times in the electrical power system [3, 4]: on 7 January, a Japan Airlines Boeing 787 caught fire on the tarmac at Boston Airport due to a battery fire, causing a direct loss of $600 million [5]; then on 16 January, another Boeing 787 made an emergency landing at Takamatsu Airport after a battery failure, which triggered a safety warning in the cockpit [6]. In fact, as early as the test flight stage in September 2010, the aircraft also experienced serious failures of electric panel fires and power outages. Therefore, the plane had to be grounded for an investigation, and Boeing had to revise the design until the Federal Aviation Administration (FAA) passed its review, which finally led to the modification to 50 APESs in the real world [7]. This above example of failure profoundly confirms the fact that system reliability is an attribute achieved by system design, and insufficient consideration of reliability in the design stage will lead to potential failures with unexpected consequences, which will bring endless future troubles for their operation and maintenance. Therefore, how to conduct an effective reliability assessment in the design stage (prior to manufacturing and operations) of AEPS is the key to ensuring flight safety and reducing subsequent operation and maintenance costs [8; 9]. System reliability assessment of AEPS in the design stage refers to how to build a system reliability model based on system architecture (topology structure) and then calculate each load point's power supply reliability given the failure rate of each component that composes the system [10; 11]. Some studies have been conducted on this. As a general method, failure mode and effects analysis (FMEA) is used to investigate the cause-effect failure relations within the AEPS [12]. However, FMEA is only a qualitative method and the power supply reliability of the system cannot be calculated. For a quantitative analysis on AEPS, [PERSON] et al. [13] analyzed the characteristics of fault tree, Markov chain, and Bayes' theorem in the reliability assessment of AEPS, and proposed a system reliability design tool for AEPS based on these methods. [PERSON] et al. [11] and [PERSON] et al. [14] put forward algorithms to apply the minimal cut set method to AEPS reliability analysis. Similarly, [PERSON] et al. [15] proposed applying the minimal path set method to the reliability assessment of AEPS. To overcome the limitation of traditional methods that the power supply reliability of each load point can only be computed one by one, [PERSON] et al. [16] proposed a configuration graph model to calculate the power supply reliability of all load points simultaneously in this one model. Furthermore, [PERSON] et al. [17] proposed to automatically transform the AEPS architecture into a three-layer Bayesian network, which can analyze power supply reliability in the consideration of the correlation among multiple load points. In addition, [PERSON] et al. [18] established a reliability model of AEPS considering common-cause failure [19] by using a Bayesian network. However, the methods above-mentioned are all based on the assumption that the component failure rate is constant to calculate the system power supply reliability. In practice, under the influence of variable operating environments and cognitive uncertainty, studies point out that it is more appropriate to treat the component failure rate as a random variable rather than a constant value [20; 21]. There are two main reasons: epistemic uncertainty in failures of designers, and the intrinsic individual differences of aircraft in failure performance due to the variable and different flight environment.