Statistical and Deterministic Tolerance Analysis and Synthesis Using a Unified Jacobian-Torsor Model

This paper presents a model for computer-aided tolerancing which enables to perform tolerance analysis and tolerance synthesis in both deterministic or statistical situations. The model combines the benefits of the Jacobian and torsor approaches developed for computer aided tolerancing. The proposed unified model is formulated using interval-based arithmetic. The paper describes how different solving engines of the same set of interval-based equations lead to different types of problems being solved, i.e. deterministic (worst case) or statistical problems. The paper also shows how the unified analysis model can be numerically inverted for performing synthesis calculations.