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For newly developing systems, the determination of the reliability index is an important task in the system demonstration process that determines both the system design goal and the verification requirement. However, due to the insufficient data at the beginning of the system life cycle, the problem of epistemic uncertainty cannot be ignored. Researchers have proposed several belief reliability metrics and analysis methods to quantify the epistemic uncertainty of a system, but to the best knowledge of the authors, no relevant studies have been performed on system reliability index determination. In this paper, we propose a belief reliability index determination method based on group decision‐making. Using a similar system‐based reliability index determination method, this method comprehensively considers the demands of users and the capabilities of contractors. In addition, the Delphi method and Hadamard multiplication convex combination are combined to effectively solve the epistemic uncertainty quantification problem. The Delphi method is used to find the conflicts caused by multi‐expert scoring, and the Hadamard multiplication convex combination can integrate the scoring matrix of all experts, which makes the results more reasonable. Finally, a Low‐Earth‐orbit (LEO) satellite communication system is used to verify the effectiveness of our belief reliability index determination method. [ABSTRACT FROM AUTHOR]

• The epistemic uncertainty of trigger effect in reliability evaluation is analyzed. • Uncertain theory is applied to quantify the PoF model-form uncertainty. • The uncertain degradation model of failure mechanism is built. • Belief reliability of the system with failure trigger effect is deduced. • The advantages of the new method are discovered in the engineering case. Reliability evaluation of system with dependent failure processes is a problem that draws more research attention. It is essential to quantify the epistemic uncertainty in the system for high evaluation accuracy. Trigger is one of the typical dependent failure processes. Trigger effect indicates that some events occur because of the trigger of other events. This paper studies the epistemic uncertainties in the reliability evaluation of the system with trigger effect based on uncertainty theory. The model-form uncertainty of physics of failure (PoF) model, the failure process uncertainty due to lack of knowledge and the propagation of them in the system are quantified with Belief Adjustment Factors Method (BAFM) and the Liu process. System belief reliability is evaluated by decoupling the correlations between the trigger failure mechanism and triggered failure mechanisms. A conductive slip ring in electromechanical orientation device is introduced as a case. The trigger effect and system belief reliability are analyzed. Results show that, compared with probability method, evaluation values with uncertainty method are more conservative and stable in the case.. [ABSTRACT FROM AUTHOR]

• The hybrid uncertainty includes the aleatory uncertainty and epistemic uncertainty is analyzed in DCFP. • The uncertainty random renewal reward process and arithmetic Liu process are used to describe the shock and degradation process. • The analytic formulas of system reliability models considering three types of DCFPs are derived. • A combinational algorithm is proposed to calculate system reliability. • The proposed method is proved to be an appropriate method to qualify the hybrid uncertainty in the case. Dependent competing failure process (DCFP) has been widely studied in recent years. When evaluating the reliability of DCFP system, the aleatory uncertainty due to randomness and the epistemic uncertainty due to lack of data and knowledge should be considered. In this paper, the hybrid uncertainty of DCFP system is analyzed and quantified with chance theory. The uncertainty random renewal reward process and the arithmetic Liu process are used to describe the shock and degradation process. The quantification of uncertainty propagation is realized by decoupling DCFP from the physical correlation aspect. Reliability of DCFP system considering two kinds of unilateral dependencies and mutual dependency is modeled and a combinational algorithm is proposed to solve it. Finally, the DCFP effect in control system of an aircraft is studied as a case, aleatory uncertainty and epistemic uncertainty are modeled, and the system reliability is evaluated. Meanwhile, the effects of key parameters on system reliability are discussed. Results show that the chance theory is an appropriate method to qualify the hybrid uncertainty for engineering systems when data is insufficient. The mutual dependency of soft failure and hard failure will reduce the system reliability. The smaller the parameter of hard failure, the greater the influence of mutual dependency on the results. [ABSTRACT FROM AUTHOR]