We propose a methodology in this study for the analysis and the optimization of assembly tolerances. A combination of three components, it involves the use of 3D CAT software, a table referred to as a "dimensional hierarchization matrix", and a tolerance optimization algorithm. The Antolin Group, a Spanish multinational in the automobile components sector, employs this system to optimize tolerance values and to reduce manufacturing costs. The matrix was designed to enable easy identification, in a single table, of all requirements that fail to meet the specifications in the different approximations, prior to the definition of the dimensional and the geometric tolerances that comply with the functional requirements, and to identify which tolerances contribute most to variations in all of the functional conditions of the mechanism. Through its different iterations, this matrix allows us to see which of the tolerances should first be modified to optimize the design requirement specifications. A tolerance optimization algorithm was also defined, which functions with the data from the dimensional hierarchization matrix.