The APTA method for the tolerance analysis of products – comparison of capability-based tolerance and inertial tolerance

Abstract

In mass production, tolerance analysis is a very important but complex task to assess the impact of allowed geometrical deviations on the functionality of the assembled products. In the design stage, the result of tolerance analysis can be a predicted defect probability expressed in ppm (parts per million) which value is highly dependent on the probabilistic modeling of dimension deviations. Tolerance analysis meets a double problem. The first one is the geometrical description of deviations and the second one is the associated statistical model. This paper focuses on this second issue. It proposes a relevant probabilistic model of each dimension deviation since no measure is available in the design stage. Lots of authors have proposed to compute the defect probability from one particular production batch with assumptions on probabilistic laws, on mean values and on standard deviations in order to assess what we call, in this paper, a conditioned defect probability. Due to tool wear, tool settings, material variations, … the production batches have variable probabilistic characteristics. The APTA methodology [2], proposed by the authors, aims at considering all the allowable production batches in the defect probability prediction thanks to a joint density function. The aims of this paper are to present the bases of the APTA methodology, to prove that it works for usual capability-based tolerance and inertial tolerance [3] and to compare both tolerance approaches on applications