APTA: advanced probability-based tolerance analysis of products

In mass production, the customer defines the constraints of assembled products by functional and quality requirements. The functional requirements are expressed by the designer through the chosen dimensions, which are linked by linear equations in the case of a simple stack-up or non-linear equations in a more complex case. The customer quality requirements are defined by the maximum allowable number of out-of-tolerance assemblies. The aim of this paper is to prove that quality requirements can be accurately predicted in the design stage thanks to a better knowledge of the statistical characteristics of the process. The authors propose an approach named Advanced Probability based Tolerance Analysis (APTA), assessing the defect probability (called P D ) that the assembled product has of not conforming to the functional requirements. This probability depends on the requirements (nominal value, tolerance, capability levels) set by the designer for each part of the product and on the knowledge of production devices that will produce batches with variable statistical characteristics (mean value, standard deviation). The interest of the proposed methodology is shown for linear and non-linear equations related to industrial products manufactured by the RADIALL SA Company.