Abstract: The current gear reliability modeling and analysis methods only consider the effect of aleatory uncertainty, and ignore the impact of epistemic uncertainty due to lack of knowledge on reliability analysis results. In this paper, the procedure and algorithm of belief reliability calculation based on performance margin are presented. The epistemic uncertainty of some design parameters and influence factors of gears are described by the uncertainty theory, the reliability of gear’s contact fatigue and bending fatigue are calculated， and the parameter sensitivity is analyzed. Besides, the reliability without considering epistemic uncertainty is compared with the above belief reliability, which further illustrates the necessity of considering epistemic uncertainty.

Key words: gear, contact fatigue, bending fatigue, epistemic uncertainty, belief reliability