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Purpose: The purpose of this paper is to present a new efficient method for the tolerance–reliability analysis and quality control of complex nonlinear assemblies where explicit assembly functions are difficult or impossible to extract based on Bayesian modeling. Design/methodology/approach: In the proposed method, first, tolerances are modelled as the random uncertain variables. Then, based on the assembly data, the explicit assembly function can be expressed by the Bayesian model in terms of manufacturing and assembly tolerances. According to the obtained assembly tolerance, reliability of the mechanical assembly to meet the assembly requirement can be estimated by a proper first-order...