In mass production, the customer defines the constraints of assembled products byfunctional and quality requirements. The functional requirements are expressed by thedesigner through the chosen dimensions, which are linked by linear equations in the caseof a simple stack-up or non-linear equations in a more complex case. The customer qualityrequirements 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 inthe design stage thanks to a better knowledge of the statistical characteristics of theprocess. The authors propose an approach named Advanced Probability based ToleranceAnalysis (APTA), assessing the defect probability (called PD)that the assembled product has of not conforming to the functional requirements. Thisprobability depends on the requirements (nominal value, tolerance, capability levels) setby the designer for each part of the product and on the knowledge of production devicesthat will produce batches with variable statistical characteristics (mean value, standarddeviation). The interest of the proposed methodology is shown for linear and non-linearequations related to industrial products manufactured by the RADIALL SA Company.