The importance of proper geometric dimensioning and tolerancing as a means of expressing the designer's functional intent and controlling the inevitable geometric and dimensional variations of mechanical parts and assemblies, is becoming well recognized. The research efforts and innovations in the field of tolerancing design, the development of supporting tools, techniques and algorithms, and the significant advances in computing software and hardware all have contributed to its recognition as a viable area of serious scholarly contributions. The field of tolerancing design is successfully making the transition to maturity where deeper insights and sound theories are being developed to offer explanations, and reliable implementations are introduced to provide solutions. Machine designers realized very early that manufacturing processes do not produce the nominal dimensions of designed parts. The notion of associating a lower and an upper limit, referred to as tolerances, with each dimen­ sion was introduced. Tolerances were specified to ensure the proper function of mating features. Fits of mating features included clearances, location fits, and interference fits, with various sub-grades in each category assigned a tolerance value depending on the nominal size of the mating features. During the inspection process, a part is rejected if a dimension fell outside the specified range. As the accuracy requirements in assemblies became tighter, designers had to consider other critical dimensions and allocate tolerances to them in order to ensure the assembly's functionality.