This paper presents a comparison of degree of freedom (DOF) based math models, viz., tolerance-maps, deviation domain, and TTRS, which have shown most potential for retrofitting the nuances of the ASME/ISO tolerance standards. Tolerances specify allowable uncertainty in dimensions and geometry of manufactured products. Due to these characteristics and application of tolerances, it is necessary to create a math model of tolerances in order to build a computer application to assist a designer in performing full 3D tolerance analysis. Many of the current efforts in modeling tolerances are lacking, as they either do not completely model all the aspects of the ASME/ISO tolerance standards or are lacking the requisite full 3-D tolerance analysis. Some tolerance math models were developed to suit CAD applications used by the designers while others were developed to retrofit the ASME/ISO tolerance standard. Three math models developed to retrofit the ASME/ISO standard, tolerance-maps, deviation domain, and TTRS are the main focus of this paper. Basic concepts of these math models are summarized in this paper, followed by their advantages and future issues. Although these three math models represent all aspects of the ASME/ISO tolerance standard, they are still lacking in one or two minor aspects.

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