The traditional reliability analysis methods based on probability theory and fuzzy set theory have been widely used in engineering practice. However, these methods are unable directly measure the uncertainty of mechanism reliability with uncertain variables, i.e., subjective random and fuzzy variables. In order to address this problem, a new quantification method for the mechanism reliability based on chance theory is presented to simultaneously satisfy the duality of randomness and the subadditivity of fuzziness in the reliability problem. Considering the fact that systems usually have multilevel performance and the components have multimode failures, this paper proposes a chance theory based multi-state performance reliability model. In the proposed method, the chance measure is adopted instead of probability and possibility measures to quantify the mechanism reliability for the subjective probability or fuzzy variables. The hybrid variables are utilized to represent the random and fuzzy parameters, based on which solutions are derived to analyze the chance theory based mechanism reliability with chance distributions. Since the input parameters of the model contain fuzziness and randomness simultaneously, an algorithm based on chance measure is designed. The experimental results on the case application demonstrate the validity of the proposed method.