Composing Distribution Function Zones For Statistical Tolerance Analysis

More and more often in industry practical exigencies force the designer to specify part tolerances statistically. Since most products are assemblies of parts, in order to assess the part-level designs he must consider their assembly-level implications. In particular, he must be able to combine specified part-level variabilities to obtain an assembly-level variability. In the simplest situation it is assumed that the populations of parts are statistically independent and that the relevant part-level values combine linearly to produce a linear gap function. Even this simplest case has wide applicability. In ISO two approaches for statistically specifying mechanical parts are being discussed. One of these defines acceptability of a population of parts by requiring that the distribution function of the relevant values of the parts be pounded by a pair of specified distribution functions. For this approach to be useful, then, a method to compose part- level specifications to yield assembly-level description is required. This paper supplies such a method for the case of statistically independent populations of parts and linear gap functions.