The statistical gauge in geometrical verification: Part I. Field of probability of the presence of matter

Currently, most measurement and geometrical verification processes are based on the characterization of distances or angles between geometrical elements. In a previous paper, a method was developed for the verification of ISO specifications using the statistical information included in a set of points. This method is based on the development of measurement sequences and hence a sequence of geometrical constructions. The main problem in this verification process is to propagate uncertainties. With a correct expression of a virtual gauge, it is possible to avoid this propagation; indeed by using virtual gauge manipulation, initial best-fitted surfaces are never touched. The aim of this paper is to present a new approach using this statistical information to describe the measured part and develop a virtual gauge system for verification. This will be done in two parts. The first part will focus on the statistical modelling of the measured surface; the second part will describe a verification method based on a virtual, i.e. numerical, gauge.