| A probability model for conducting statistical tolerance analysis and allocation is put forth in this dissertation. The model utilizes the ASU T-Maps model for geometric tolerances to build the frequency distribution for a dimension of interest in an assembly of parts. The central element of the ASU T-Maps model is the Tolerance-MapRTM (T-Map RTM); it is the range of points resulting from a one-to-one mapping from all the variational possibilities arising from the manufacture of a feature, within its tolerance-zone, to a specially designed Euclidean point-space. A functional T-Map represents both the acceptable range of one-dimensional dimension of interest and the acceptable limits to the three-dimensional variational possibilities of the target feature consistent with it. An accumulation T-Map represents all the accumulated three-dimensional variational possibilities of the target feature which arise from allowable variations on the individual parts in the assembly. The geometry of the target feature and a specific value of the dimension of interest are used to establish a functional surface that intersects the accumulation T-Map. The common points to the geometric shapes of the accumulation T-Map and the functional surface provide a measure of all variational possibilities of manufacture of the parts, which will give the specific value of the dimension of interest. By choosing many values of the dimension of interest, the measures are then arranged as a probability density function.;Since, the ASU Tolerance-Map model is in conformance with alternate and supplemental specifications for tolerances in the ASME Y14.5 standard, the probability model also gives distinct results for each alternative and added refinement. The probability model from T-Maps presented in this thesis builds the probability distributions from the geometric bias of the tolerance zone and measurement type, while assuming equal likelihood of manufacturing biases. If consistent experimental data are available correlating the manufacturing biases to the position, orientation and form of a feature, these manufacturing biases can be included as weights when constructing the frequency distributions.;The probability model is applied to several assemblies that contain planar features, an engaged pin and hole, an engaged tab and slot, a feature-cluster, and patterns of features. The results are compared with those from Monte Carlo simulations in commercial software. |
