Measuring the errors of form of industrial surfaces: prediction and optimization

To acquire maximum information on the geometrical errors of industrially made surfaces at a minimum cost, a method for estimating conditional probabilities of a random signal (Bayesian prediction) is applied to three-dimensional metrology. First, a surface is interpolated between data acquired on a coordinate measuring machine (CMM). Then, for a given probability, limit surfaces are computed that bind a region of space containing the known data and the most probable interpolation of the missing data of the surface. These bounds can be treated as the surface; their points can be considered as if they were actual CMM data when fitting a tolerance zone or a datum feature to the data. For Bayesian prediction, the basic hypotheses on the signal are stationarity, ergodicity, and gaussian density. Deviations from these hypotheses and their consequences on the prediction are taken into account and corrections are proposed.