Purpose The conventional statistical method of three-dimensional tolerance analysis requires numerous pseudo-random numbers and consumes enormous computations to increase the calculation accuracy, such as the Monte Carlo simulation. The purpose of this paper is to propose a novel method to overcome the problems. Design/methodology/approach With the combination of the quasi-Monte Carlo method and the unified Jacobian-torsor model, this paper proposes a three-dimensional tolerance analysis method based on edge sampling. By setting reasonable evaluation criteria, the sequence numbers representing relatively smaller deviations are excluded and the remaining numbers are selected and kept which represent deviations approximate to and still comply with the tolerance requirements. Findings The case study illustrates the effectiveness and superiority of the proposed method in that it can reduce the sample size, diminish the computations, predict wider tolerance ranges and improve the accuracy of three-dimensional tolerance of precision assembly simultaneously. Research limitations/implications The proposed method may be applied only when the dimensional and geometric tolerances are interpreted in the three-dimensional tolerance representation model. Practical implications The proposed tolerance analysis method can evaluate the impact of manufacturing errors on the product structure quantitatively and provide a theoretical basis for structural design, process planning and manufacture inspection. Originality/value The paper is original in proposing edge sampling as a sampling strategy to generating deviation numbers in tolerance analysis.

Purpose The purpose of this paper is to propose a novel mathematical model to present the three-dimensional tolerance of a discrete surface and to carry out an approach to analyze the tolerance of an assembly with a discrete surface structure. A discrete surface is a special structure of a large surface base with several discrete elements mounted on it, one, which is widely used in complex electromechanical products. Design/methodology/approach The geometric features of discrete surfaces are separated and characterized by small displacement torsors according to the spatial relationship of discrete elements. The torsor cluster model is established to characterize the integral feature variation of a discrete surface by integrating the torsor model. The influence and accumulation of the assembly tolerance of a discrete surface are determined by statistical tolerance analysis based on the unified Jacobian-Torsor method. Findings The effectiveness and superiority of the proposed model in comprehensive tolerance characterization of discrete surfaces are successfully demonstrated by a case study of a phased array antenna. The tolerance is evidently and intuitively computed and expressed based on the torsor cluster model. Research limitations/implications The tolerance analysis method proposed requires much time and high computing performance for the calculation of the statistical simulation. Practical implications The torsor cluster model achieves the three-dimensional tolerance representation of the discrete surface. The tolerance analysis method based on this model predicts the accumulation of the tolerance of components before their physical assembly. Originality/value This paper proposes the torsor cluster as a novel mathematical model to interpret the tolerance of a discrete surface.