||This paper reports two different approaches to the analysis of tolerance chains. A simple part is considered and a functional dimensioning scheme is described. Then, an analysis of the tolerances is performed with a commercial software package and with a methodological statistical procedure. In particular, the procedure proposed can be summarised into two main steps. First, each single technological operation (for example, the drilling of a hole) is simulated by extracting, from a statistical distribution typical of the machine tool, the parameters characteristic of the manufacturing procedure. Then, a simulation is performed, to verify if the real features of the part can simultaneously fit the virtual gage. This method of acceptance/rejection of a part is according to the ISO/ASME standards and is representative of the real functional requirements of the part.