## 1 Introduction  
With progress in science and technology, the focus on the effect of uncertainty has received increasing attention in engineering design. As an indispensable ingredient of reliability-based multidisciplinary design optimization (RBMDO), the multidisciplinary analysis (MRA) plays a decisive role in evaluating the reliability of multidisciplinary systems. In RBMDO, the probabilistic model on basis of a large amount of statistical data is the most common method to quantify aleatory uncertainty and it has achieved great success [1; 2]. With the development of artificial intelligence technology, some machine learning and advanced statistical framework, such as probability boxes [3], are introduced into the field of reliability evaluation. [PERSON] et al. [4] proposed a deep reinforcement learning-based sampling method for reliability analysis, which uses a deep neural network as agent to select test points automatically and construct the surrogate model for reliability assessment. [PERSON] et al. [5] proposed a Bayesian surrogate learning for reliability analysis, which increases the minimum number of possible samples from various disciplines to achieve accurate and reliable uncertainty propagation in coupled multidisciplinary systems. These methods all need enough statistical information. However, the lack of statistical data often makes it difficult to quantify the statistical distribution of the design parameters. It is incapable of obtaining credible results for a probabilistic model, so non-probabilistic models such as convex models are used to quantify single interval uncertainty. Actually, uncertainties are ubiquitous in each design stage of complex engineered systems, which can be classified into aleatory uncertainty (AU) and epistemic uncertainty (EU) according to human cognition [6]. Aleatory uncertainty is also known as random uncertainty, stochastic uncertainty and irreducible uncertainty. It describes the internal changes of the physical system and has sufficient test data and perfect information. Conversely, the epistemic uncertainty is affected by negligence, experimental conditions or other cognitive ability caused by the lack of knowledge and imperfect information, so it is also known as reducible uncertainty, subjective uncertainty, etc. Many scholars have studied some reliability analysis methods considering interval or other epistemic uncertainties. Fuzzy theory [7], possibility theory [8], evidence theory [9] and convex set theory [10] have been used to quantify epistemic uncertainty and to conduct reliability analysis. In many circumstances, both aleatory and epistemic uncertainties coexist in the complex and coupled multidisciplinary systems. According to different analysis principles, the current reliability analysis methods under mixed uncertainties can be divided into \"transformation type\" and \"analysis type\". \"Transformation type \"refers to transforming different uncertainty variables into the same type of uncertainty variables, and then using the reliability analysis method under a single type of uncertainty for analysis. Researchers such as [PERSON] et al. [11] transformed random variables into fuzzy variables according to the principle of probability possibility consistency and the most conservative condition. [PERSON] et al. [12] used evidence theory and random expansion method to study the uncertainty of implicit state when random variables and interval variables exist at the same time. While, \"analysis type\" refers to the analysis of system reliability by different uncertainty quantification theories without any transformation for the mixed uncertainties. Researchers such as [PERSON] et al. [13] have established the conditional possibility model of failure based on probability/possibility theory, and analyzed the reliability based on the principle of cut set.