This paper presents a methodology to enable the tolerances on mating parts of an assembly to be specified and be compatible to the precision of an assembly robot so as to achieve maximum system performance. The measure of performance is defined as the Probability of Successful Assembly (PSA). A typical loose fastener assembly, usually called peg-in-a-hole is investigated. The Geometric Tolerancing System is adopted to represent position tolerances of mating parts. Two models are presented by considering modifiers on a position tolerance, Regardless of Feature Size (RFS) and Maximum Material Condition (MMC). Using these models, it is analyzed how the Standard Limits and Fits recommended by ANSI influence the performance of an assembly robot. For this analysis, the Standard Limits and Fits are transformed to the representation scheme of the Geometric Tolerancing System. Due to low PSAs when the Standard Limits and Fits are taken into account, the effect of chamfers around a hole is also analyzed.