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In reliability engineering, the observations of the variables of interest are always limited due to cost or schedule constraints. Consequently, the epistemic uncertainty, which derives from lack of knowledge and information, plays a vital influence on the reliability evaluation. Belief reliability is a new reliability metric that takes the impact of epistemic uncertainty into consideration and belief reliability distribution is fundamental to belief reliability application. This paper develops a new method called graduation formula to construct belief reliability distribution with limited observations. The developed method constructs the belief reliability distribution by determining the corresponding belief degrees of the observations. An algorithm is designed for the graduation formula as it is a set of transcendental equations, which is difficult to determine the analytical solution. The developed method and the proposed algorithm are illustrated by two numerical examples to show their efficiency and future application.

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