###### Abstract  
In practical applications, the multidisciplinary dynamic system design optimization (MDSDO)-based solution is limited by uncertainty, which causes random variation in the physical design variable in the static discipline and the equation of state in the dynamic discipline. To address the lack of reliability of the MDSDO solution, a crossrate-based MDSDO approach (C-MDSDO), consisting of the MDSDO stage and a reliability assessment stage, is proposed in this paper. In the reliability assessment stage, a sub-optimization problem based on the crossrate of the objective reliability index sample trajectory is designed to obtain the shifting vector, which is employed to obtain a sufficiently reliable solution. In addition, the proposed approach adopts a sequential problem-solving framework that avoids nested optimization and a reliability assessment. One numerical case and two engineering cases were employed to validate the effectiveness of the proposed method. The results show that the reliability of the proposed solutions significantly improved. multidisciplinary dynamic system design optimization; sequential approach;  
control problem is converted into a boundary value problem [15; 16]. In the direct approach, i.e., direct transcription (DT), the control problem is converted into nonlinear programming (NLP) using discrete control and state variables at the time nodes. Typical direct approaches include control vector parameterization and orthogonal collocation [17; 18]. The design approaches for the static and dynamic disciplines are fairly well developed and enable the optimal solution to be obtained for each discipline. However, it is difficult to obtain the optimal solution for a whole system with a split design process [9]. Therefore, researchers proposed the multidisciplinary dynamic system design optimization (MDSDO) theory by introducing the concept of integrated design. [PERSON] et al. coupled the optimization process of static and dynamic disciplines to form the nested optimization algorithm [19]. Furthermore, various researchers constructed the surrogate model of the right-hand-side function of the state equation in the inner dynamic discipline optimization loop, which significantly improves the efficiency of the inner loop and overcomes the inefficiency of the nested algorithm [20; 21; 22]. Moreover, other researchers employed the simultaneous optimization approach [23; 24]. The research on MDSDO is still in its developmental stage, and its problem-solving approaches need to be further improved. In the static discipline of an MDSDO problem, design variables may vary because of certain known or unknown factors, which is known as the \"uncertainty\". To avoid the negative effects associated with uncertainty in design approaches using static disciplines, researchers proposed reliability-based design optimization (RBDO) [25; 26], which assesses the deterministic solution and improves its reliability based on the assessment result. In addition, the practicality of the approach is significantly enhanced by further improvements [27; 28]. Since the static discipline is an essential part of MDSDO, introducing the reliability assessment also acts to improve reliability-based design optimization for the MDSDO problem. The findings related to reliability-based MDSDO remain limited. Some researchers propose a three-loop framework, in which the reliability assessment is directly nested in the static discipline design loop [29]. However, as the complexity of the problem increases, the efficiency of this nested framework becomes insufficient. Certain researchers propose a transformation-based reliability-based MDSDO framework by transforming the uncertainty design variables into equivalent deterministic and concomitant variables and adding equality constraints in the optimization process of the dynamic discipline [30].